The acceleration due to gravity g is plotted against the latitude of a place. Out of the following, the one that best represents the graph is
Find the angular momentum of satellite of mass 400 kg moving around the earth in radius 4 x 10 7 m.
A satellite is moving around the earth in a circular orbit. Radius of the orbit is r and kinetic energy is K. Another satellite is moving around the earth in circular orbit of radius 2r. Then total energy of the second satellite is
A particle of mass 10g is kept on the surface of a uniform sphere of mass 100kg and radius 10cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere is (G=6.67x 10 -11 Nm 2 kg -2 )
A spaceship is launched into a circular orbit of radius R close to the surface of the earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth’s gravitational pull is (g → acceleration due to gravity)
Two identical point masses are placed at a separation of d. Out of the following graphs the graph that represents the variation of gravitational field intensity E with the distance r from any one mass to the other along the line joining them is
Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final-initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R), is given by ?
The speed of earth’s rotation about its axis is ω Its speed is increases to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is
The escape velocity corresponding to a planet of mass M and radius R is 50 km/sec. If the planet’s mass and radius were 4M and R respectively then the corresponding escape velocity would be
A body is projected vertically upwards from the surface of a planet of radius fl with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is
Kepler’s third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T 2 = K r 3 here K is constant. If the masses of sun and planet are M and m respectively then as per Newton’s law of gravitation force of attraction between them is F = G M m r 2 , here G is gravitational constant. The relation between G and K is described as
What is the depth at which the value of acceleration due to gravity becomes 1 n times the value that at the surface of earth? (radius of earth = R)
A body is projected up with a velocity equal to 3/4th of the escape velocity from the surface of earth. The height it reaches is (R=Radius of earth)
A satellite of mass m is in circular orbit of radius 3 R E about earth (mass of earth M E , radius of earth R E ). How much additional energy is required to transfer the satellite to an orbit of radius 9 R E ?
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances.1m, 2 m, 4 m, 8 m,…. respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
The escape velocity of a body from the surface of the earth is nearly
A body projected vertically from the earth reaches height equal to earth’s radius before returning to the earth, The power exerted by the gravitational force is greatest
Imagine a light planet is revolving round a very massive star in a circular orbit of radius R with a time period of revolution T. If the gravitational force of attraction between the star and planetis proportional to R -n , then T 2 is proportional to
A particle falls towards the earth from infinity. The velocity with which it reaches earth’s surface (g → acceleration due to gravity on earth’s surface and R is the radius of the earth)
If a body is projected with speed less than escape velocity, then a) the body can reach a certain height and may fall down following straight line path b) the body can reach a certain height and may fall down following a parabolic path c) the body may orbit the earth in a circular path d) the body may orbit the earth in an elliptical path.
A satellite of mass “m” orbits a planet “P” in an elliptical orbit. The satellite is then transferred to another circular orbit of radius “r” as shown in the figure. Which of the following hold true in this scenario?
Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific density 3. The gravitational force will now be :
In some region of space, gravitational field is given by − C r , r being the distance and C a constant. At a certain value of r = r 0 , gravitational potential is V’. General expression of gravitational potential as a function of r is :
The value of g will be 1% of its value at the surface of earth at a height of (R e = 6400 km) :
If the acceleration due to gravity at earth is ‘g’ and mass of earth is 80 times that of moon and radius of earth is 4 times that of moon, the value of ‘g’ at the surface of moon will be :
What should be the angular velocity of earth about own axis so that a person’s weight at equator will be 3 5 of his weight at poles?
How much deep inside the earth (radius R) should a man go, so that his weight becomes one-fourth of that on earth’s surface?
If g is the acceleration due to gravity on earth’s surface, the gain of the potential energy of an object of mass m raised from the surface bf the earth to a height equal to the radius R of the earth is :
With what velocity should a particle be projected so that its height becomes equal to radius of earth?
Inside a uniform spherical shell : (i) potential is zero (ii) field is zero (iii) potential is constant (iv) field is constant
The escape velocity from a spherical planet is v o . What is the escape velocity corresponding to another planet of twice the radius and half the mean density?
The escape velocity of a body on an imaginary planet which is thrice the radius of the earth and double the mass of the earth is (v o is the escape velocity of earth)
The escape velocity from the earth is 11 km/s. The escape velocity from a planet having twice the radius and same mean density as that of earth is :
A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km/sec, escape velocity from the surface of the planet would be :
The escape velocity of a projectile on the earth’s surface is 11.2 km s -1 . A body is projected out with thrice this speed. The speed of the body far away from the earth will be :
Let A and B be the points respectively above and below the earth’s surface each at a distance equal to half the radius of the earth. If the acceleration due to gravity at these points be g A and g A respectively, then g B : g A is :
A satellite is projected with a velocity 1.5 times the orbital velocity just above the surface of earth. Initial velocity of the satellite is perpendicular to the surface of earth. The maximum distance of the satellite from surface of earth will be
Find net ‘F G ’ of any one of the given figure.
A particle is dropped from height 3R from surface of earth. Then, the velocity of particle at height R is (given R is radius of earth, g is acceleration due to gravity on the earth’s surface) :
A mass m is at a distance a from one end of a uniform rod of length l and M. The gravitational force on the mass due to the rod is
The masses, each of mass m are kept on the vertices of an equilateral triangle of side a. Find the work needed to be done to change the length of each side of the triangle twice of its original value.
A cavity of radius R/2 is made inside a solid sphere of radius R. The centre of the cavity is located at a distance R/2 from the centre of the sphere. The gravitational force on a particle of mass ‘m’ at a distance R/2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of cavity) [Here g = GM / R 2 , where M is the mass of the sphere]
The work done to raise a mass m from the surface of the earth to a height h , which is equal to the radius of the earth, is
A body of mass ‘m’ is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be
The orbital angular momentum of a satellite revolving at a distance r from the centre is L. If the distance is increased to 16r, then the new angular momentum will be
Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final – initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R), is given by,
A satellite can be in a geo stationary orbit around a planet at a distance r from the centre of the planet. If the angular velocity of the planet about its axis doubles, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is
The gravitational potential due to earth at infinite distance from it is zero. Let the gravitational potential at a point P be -5 J k g – 1 . Suppose, we arbitrarily assume the gravitational potential at infinity to be +10 J k g – 1 , then the gravitational potential at P will be
A satellite ‘A’ is moving in a circular orbit of radius ‘r’ around the earth with orbital speed V. Another satellite B is moving in a circuit orbit of radius 2r. If areal velocities of A and B are equal, Then orbital speed of B is
Escape velocity on the surface of a planet of radius R and density ρ is V. What will be the escape velocity on the surface of a planet of radius 2R and density 4 ρ ?
A satellite of mass m is moving in a circular orbit with speed V. Then potential energy of earth satellite system is
A narrow tunnel is dug along the diameter of Earth. If g be the acceleration due to gravity on the surface of earth and R be the radius of earth, Then work done in moving an object of mass m from the centre of earth to its surface is
A particle of mass m is placed at the centre of a thin spherical shell of mass 2m and radius R. Then the gravitational potential at a distance R 2 from the centre of the shell is
Densities of two planets are in the ratio 1 : 2 and their radii are in the ratio 3 : 1. Then the ratio of time periods of a simple pendulum of their surfaces are in the ratio.
The kinetic energies for a planet in an elliptical orbit about the sun, at positions A, B and C are K A ,K B and K C , respectively. AC is the major axis and SB is perpendicular to AC at the position of the sun S as shown in the figure. Then
The weight of an object in the coal mine, sea level and at the top of the mountain are respectively W 1 , W 2 and W 3 , then
Three equal masses m are placed at the three vertices of an equilateral triangle of side a.The gravitational force exerted by this system on another particle of mass m placed at the midpoint of a side
Assuming the earth to be a uniform sphere of mass M and radium R. which of the following graphs represents the variation of acceleration due to gravity with distance ‘r’ from the centre of the earth.
Weight of a body on the surfaces of two planets is the same. If their densities are d 1 and d 2 , then the ratio of their radius
Two artificial satellites A and B of same mass are revolving round the earth at heights h 1 and h 2 in circular orbits. If h 2 < h 1 , the satellite possessing greater K.E. is
The amount of work done in lifting a body of mass ‘m’ from the surface of the earth to a height equal to twice the radius of the earth is
The value of acceleration due to gravity on the surface of earth is x. At alttitude of ‘h’ from the surface of earth, its value is y. If ‘R’ is the radius of earth, then the value of h is
When a projectile attains the escape velocity, then on surface of planet its
The PE of a satellite is –U. Its KE is
Inside a satellite orbiting very close to the earth’s surface, water does not fall out of a glass when it is inverted. Which of the following is the best explanation for this ?
An artificial satellite of the earth releases a packet. If air resistance is neglected, the point where the packet will hit, will be
The escape velocity for a planet is . A particle is projected horizontally from the top of tower of height h with a speed . For this particle to move as a satellite around the planet
The magnitude of potential energy per unit mass of the object at the surface of earth is ‘E’. Then escape velocity of the object is
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth of below the surface of earth. Then:
The radius in kilometers to which the present radius of the earth (R=6400 km) is to be compressed so that the escape velocity is increases to ten times is
The ratio of escape velocity at the surface of earth to the escape velocity at the surface of a planet whose radius and mean density are twice as that of earth is
The minimum and maximum distance of a satellite from the centre of the earth 2R and 4R respectively. Where R is the radius of the earth and M is the mass of earth. Its maximum speed is
A small body is projected from the earth’s surface vertically up with the escape velocity on the earth.Out of the following curves the one that represents the variation of KE with altitude h is
One can easily weighs the earth by calculating the mass of the earth by using the formula (in usual notation)
The escape velocity of a body on the earth’s surface is ve. A body is thrown up with a speed of kve, where k >1, Assuming that the sun and planets do not influence the motion of the body, then the velocity of the body at the infinite distance is
Among the following find the wrong statement
If the earth shrinks to half of its radius and mass remains constant, then the weight of an object on earth will become
Mass of the earth is 81 times that of the moon. If the distance between their centers is d, then the point on the line joining their centers at which the gravitational field due to them is zero is
P is a point at a distance r from the centre of a solid sphere of radius a. The gravitational potential at P is V. If V is plotted as a function of r, which is the correct curve ?
A spherical planet far out in space has a mass M 0 and diameter D 0 . A particle of mass ‘m’ falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to
A satellite appears to be at rest when seen from the equator of the earth. The height of the satellite from the surface of the earth is
A body is released from a height R/2 above the surface of earth where R is the radius of earth. If g be the acceleration due to gravity on the surface of earth, velocity of the body just before it strikes the surface of earth is
Weight of a body on the surface of earth is 100 N. If R be the radius of earth, then what will be the weight of the body at a height R/2 above the surface of earth?
The earth is able to retain its atmosphere because of
Three particles, each of mass M are moving in a circle under their mutual gravitational forces such that they always form an equilateral triangle of side a while rotating. Speed of each particle is:
At what distance from the centre of the moon is the point at which the strength of the resultant field of earth’s and moon’s gravitational fields equal to zero? The earth’s mass is 81 times that of moon and the distance between centres of these planets is 60 R where R is the radius of earth :
Acceleration due to gravity decreases as we go up from the surface of the earth. Then in going below the surface of the earth it :
Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by :
The height at which the acceleration due to gravity becomes g 9 (where g = the acceleration due to gravity on the surface of the earth) in erms of R, the radius of the earth is :
The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be :
A particle is projected vertically upwards with a speed V 0 from the surface of the earth. The maximum height reached by the particle is equal to radius R of the earth. If g be the acceleration due to gravity on the surface of the earth, then :
Given that mass of earth is M and its radius is R. A body is dropped from a height equal to the radius of earth above the surface of earth. When it reaches the ground, its speed will be:
An asteroid of mass m is approaching earth, initially at a distance of 10 R e with speed v i . It hits the earth with a speed v f (R e and M e are radius and mass of earth), then :
The escape velocity of a body projected vertically upwards from the earth’s surface is 11.2 km/sec. If the body is projected in a direction making 30° angle to the vertical, its escape velocity in this case will be :
The escape velocity of a particle of mass m varies as :
Two bodies of masses M 1 , and M 2 are kept separated by a distance d. The potential at the point where the gravitational field produced by them is zero, is :
The gravitational force between two bodies is 6.67 x 10 -7 N when the distance between their centres is 10m. If the mass of first body is 800 kg, then the mass of second body is
Mass M=1 unit is divided into two parts X and (1–X). For a given separation the value of X for which the gravitational force between them becomes maximum is
If g is the acceleration due to gravity on the earth’s surface, the change in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is
A uniform spherical shell of radius R, has mass m. Two other point masses of mass m each, are kept at point P and Q respectively. If the force of interaction between the shell and the point mass at p is F 1 and between the shell and the point mass at Q is F 2 . Find F 1 F 2 .
The gravitational potential energy in a region of space is given by U ( x , y ) = − 3 x 2 y + xy . Find the acceleration of a particle of mass 100g at (1,2)
A body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity. If fi is the radius of the earth, the maximum height attained by the body is
Suppose g e be the acceleration due to gravity at the equator and g p be that at the poles’ Assuming earth to be a sphere of radius R e rotating about its own axis with angular speed ω the g p , – g e , is given by
Which of the graphs fig. represents correctly the variation of intensity of gravitational field I with the distance r from the centre of a spherical shell of mass M and radius a ?
Mass of moon is 7 ⋅ 34 × 10 22 kg If the acceleration due to gravity on the moon is 1 ⋅ 4 m / s 2 the radius of the moon is G = 6 ⋅ 667 × 10 − 11 Nm 2 / kg 2
The magnitudes of gravitational field at distances r 1 and r 2 from the centre of a uniform sphere of radius R and mass M are F 1 and F 2 , respectively. Then
Three identical bodies of equal mass m each moves along a circle of radius .R under the action of their mutual gravitational attraction. The speed of each body is
The density of newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be
For a satellite moving in an orbit around the earth, the ratio of kinetic energy to the magnitude of potential energy is
Two particles of mass m and M are initially at rest and infinitely separated from each other. Due to mutual interaction they approach each other. Their relative velocity of approach at a separation distance d between them is
A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 x 10 24 kg) have to be compressed to be a black hole?
Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by
A uniform ring of mass m is lying at a distance 3 a form the centre of a sphere of mass M just over the sphere (where a is the radius of the ring as well as that of the sphere). Then magnitude of gravitational force between them is
If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?
A satellite going round the earth in a circular orbit loses some energy due to a collision. Its speed is v and distance from the earth is d, then
A remote-sensing satellite of earth revolves in a circular orbit at a height of 0 . 25 × 10 6 m above the surface of earth. If earth’s radius is 6 . 38 × 10 6 m and g = 9 . 8 ms – 2 , then the orbital speed of the satellite is
A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth?
A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m, 2 m, 4 m, 8 m, …, respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the sun are r 1 a n d r 2 respectively. The time-period of the planet is proportional to
The magnitude of the gravitational field at distance r 1 a n d r 2 from the centre of a uniform sphere of radius R and mass M are F 1 a n d F 2 respectively. Then
Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by
A satellite of mass m is orbiting the earth (of radius R ) at a height h from its surface. The total energy of the satellite in
The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. V P a n d V E are escape velocities of the planet and the earth, respectively, then
A particle of mass ‘m’ is kept at rest at a height 3R from the surface of earth, where ‘R’ is radius of earth and ‘M’ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth)
The radius of a planet is R . A satellite revolves around it in a circle of radius r with angular speed .The acceleration due to gravity on planet’s surface will be :
The rotation of the earth having radius R about its axis speeds up to a value such that a man at latitude angle 60° feels weightlessness. The duration of the day in such a case is:
Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of escape velocity V A V B is
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then
Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will
A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth ?
A satellite of mass m is at distance r from the centre of the earth. Another satellite B of mass 2m is at distance 4r from earth’s centre . Their time periods are in the ratio
A satellite is seen after every 6 hours over the equator. It is known that is rotates opposite to that of earth’s direction. Then the angular velocity ( in radians per hour) of the satellite about the centre of earth will b
The escape velocity from earth is v e . A body is projected with velocity 2 v e . With what constant velocity will it move in the inter planetary space?
Three identical point masses, each of mass 1 kg lie in the XY plane at points (0,0) , (0,0.2m) and (0.2m,0). The net gravitational force on the mass at the origin is
A mass falls from a height ‘h’ and its time of fall ‘t’ is recorded in terms of time period T of a simple pendulum. On the surface of earth it is found that t = 2T. The entire set up is taken on the surface of another planet whose mass is half of that of earth and radius the same. Same experiment is repeated and corresponding times noted as t’ and T’ . Then we can say
The time period of a geostationary satellite is 24 h, at a height 6 R E ( R E is radius of earth) from surface of earth. The time period of another satellite whose height is 2.5 R E from surface will be,
Imagine earth to be a solid sphere of mass M and radius R. If the value of acceleration due to gravity at a depth ‘d’ below earth’s surface is same as its value at a height ‘h’ above its surface and equal to g 4 (where g is the value of acceleration due to gravity on the surface of earth), the ratio of h d will be:
The period of a satellite of the earth very near to the surface of the earth is T 0 . What is the approximate period of the geostationary satellite in terms of T 0 ? (Height of geostationary satellite above the surface of earth is 36000km)
Time period of oscillation of a simple pendulum on the surface of earth is T. At what height above the surface of earth will the time period be 4T ?
A particle of mass M is at a distance ‘R’ from the surface of a thin spherical shell of mass M uniformly distributed over its surface, R is the radius of the shell. Now select the correct option.
Gravitational force is a central force which is always conservative. Which of the following forces is noncentral and conservative in nature?
If gravitational potential at an altitude ‘R’ above the surface of earth is ‘U’, Then gravitational potential at the centre of earth will be
A planet is moving in a circular orbit around earth. Then the minimum increase of its orbital speed for which the planet will escape to infinity is
Two thin rings having masses m 1 and m 2 , each of radius R, are coaxially placed at a distance R. Then the work done in moving a particle of mass m from the centre of one ring to that of the other is
Two thin spherical shells A and B, each having radius ‘R’, are kept in contact with each other as shown in figure. Then if F be the magnitude of mutual gravitational force of attraction, then
The ratio of work done in taking a body from the surface of earth (Radius = R) to a height R above the surface of earth to the work done in placing the object in a circular orbit at that height is
A satellite is revolving round the earth with orbital speed V 0 .If it stops suddenly, the speed with which it will strike the surface of earth would be ( V e = escape velocity of a particle on earth’s surface)
A spherical shell is cut into two pieces along a chord as shown in the figure. P is a point on the plane of the chord. The gravitational field at P due to the upper part is I 1 and that due to the lower part is I 2 . What is the relation between them?
Figure shows a planet in an elliptical orbit around the Sun S. Where is the kinetic energy of the planet maximum?
A satellite of mass m is revolving around the Earth of mass M in a circular orbit of radius r . As the satellite moves from one point of the orbit to the diametrically opposite point, the magnitude of change in the gravitational force it experiences is (G is universal gravitational constant)
A point P is on the axis of a fixed ring of mass M and radius R, at a distance 2R from the centre O. A small particle starts from P and reaches O under the gravitational attraction only. Its speed at O will be
Two concentric shells of masses M 1 and M 2 are having radii r 1 and r 2 r 2 > r 1 . Which of the following is the correct expression for the gravitational field on a mass m ?
A thin rod of length L is bent to form a semicircle. The mass of rod is M. What will be the gravitational potential at the centre of the circle?
Two satellites of the same mass are launched in the same orbit around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is
Two bodies of mass m and M are placed a distance d apart. The gravitational potential at the position where the gravitational field due to them is zero is V. Then :
A body is revolving very close to the surface of the planet. When mass of the planet suddenly reduced to half without any change in radius then
A satellite of mass m is moving in circular orbit around the earth with kinetic energy K and its angular momentum is L. What will be the angular momentum of a satellite of mass 4m which is moving in a circular orbit around the earth with kinetic energy 4K.
Acceleration due to gravity at the pole of earth is g, at the equator it is g n ( n > 1 ) . If R be the ratios of earth then time period of spin of earth is
A projectile is fired vertically from the surface of earth with a speed gR . Where R is the radius of earth. How far above the earth’s surface would the projectile go?
Two point masses m and 4m are at separation r. P is a point where gravitational field is zero. Then gravitational potential at point P is
Gravitational potential on the surface of a spherical planet of radius R is V. What will be the gravitational potential on the surface of another planet of radius 2R ? Both planets are made of same material.
A satellite is moving in circular orbit around the earth with orbital speed v. It radius of earth is R and acceleration due to gravity on its surface is g, then height of the satellite above the surface of earth is
A uniform solid sphere of mass m and radius r is surrounded symmetrically by a uniform thin spherical shell of radius 2r and mass m
At a height above the surface of earth (Radius = R) acceleration due to gravity is g 4 where g is the acceleration due to gravity on the surface of earth. Then gravitational potential at that height is
A particle of mass ‘m’ moves on the axis of a ring of radius ‘R’ and mass M. If particle at rest is released from ‘P’ then its kinetic energy at centre c will be
If there were a small alteration in gravitational force, then which of the following forces do you think would alter in some respect
Two identical trains A and B move with equal actual speeds on parallel tracks along the equator. A moves from east to west and B, from west to east. Which train will exert greater force on the tracks ?
Planets move round the sun due to
An infinite number of particles each of mass 1kg are placed on the positive x-axis at 1m, 2m, 4m, 8m…. from the origin. The magnitude of the resultant gravitational force on 1kg mass kept at the origin is
Two equal masses separated by a distance (d) attract each other with a force (F). If one unit of mass is transferred from one of them to the other, the force
A particle of mass m is placed inside a spherical shell, away from its centre. The mass of the shell is M.
At a certain height above the earth’s surface, the gravitational acceleration is 4% of its value at the surface of the earth. Find the height. (R is the surface of the earth)
A body weighs 700gm – wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass is 1/7 and radius half of the earth
There is no atmosphere on moon because
When a satellite is orbitting round a planet in circular orbit, workdone by the gravitational force acting on the satellite is
The radius of the earth is about 6400km and that of mars is about 3200km. The mass of the earth is about 10 times that of mars. If an object weighs 200 N on the surface of earth its weight on the surface of mars would be
The alttitude at which the weight of a body is only 64% of its weight on the surface of the earth is (Radius of the earth is 6400km)
If R is radius of the earth, the height above the surface of the earth where the weight of a body is 36% less than its weight on the surface of the earth is
The angular velocity of the earth about its polar axis so that the weight of the body at the equator will be zero is
An artificial satellite orbiting the earth does not falldown, because the earth’s attraction
A man inside an artificial satellite feels weightlessness, because the force of attraction due to earth is
A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential
An earth satellite is moved from one stable circular orbit to a farther stable circular orbit. Which one of the following quantities increases
The minimum KE required to project a body of mass ‘m’ from the earth’s surface to infinity is
The magnitude of gravitational potential energy of the moon-earth system is U with zero potential energy at infinite separation. The kinetic energy of the moon with respect to the earth is K.
A space station is set up in space at a distance equal to earth’s radius from earth’s surface. Suppose a satellite can be launched from space station. Let V 1 and V 2 be the escape velocites of the satellite on earth’s surface and space station respectively. Then
A point P lies on the axis of a ring of mass M and radius a, at a distance a from its centre C. A small particle starts from P and reaches C under gravitational attraction only. Its speed at C will be
A particle of mass M is placed at the centre of a uniform spherical shell of mass 2M and radius R. The gravitational potential on the surface of the shell is
The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth’s surface is g. What will be the radius of the orbit of a geostationary satellite ?
At what temperature, hydrogen molecules will escape from the earth’s surface ? (Take mass of hydrogen molecule = 0.34 × 10 –6 kg, Boltzmann constant = 1.38 × 10 –23 KJ –1 , Radius of earth=6.4 × 10 6 m and acceleration due to gravity=9.8 ms –2 )
An orbiting satellite will escape if a) its speed increases by 41.4% b) its speed in the orbit is made 1 . 414 times that of its initial value c) its kinetic energy increases by 100% d) its kinetic energy is made √2 times that of its initial value
A satellite is moving in a circular orbit at a height R above the surface of earth with kinetic energy K. If the satellite is suddenly stopped, with what kinetic energy will it strike the surface of earth?
Weight of a body at a height R/2 (Radius of earth = R) above the surface of earth is 80 N. What will be its weight at a depth R/2 below te surface of earth?
A body starts from rest from a point distant r 0 from the centre of the Earth. It reaches the surface of the Earth whose radius is R. The velocity acquired by the body is if r 0 > R
A body weighs 180 N on the surface of earth (Radius=R). How much does the body weigh at a height R 2 above the surface of earth?
At surface of earth weight of a person is 72 N then his weight at height R 2 from surface of earth is ( R = radius of earth)
A body weighs 700 gm wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass is 1 7 and radius is half that of the earth
On the surface of earth, the gravitational field is E g and gravitational potential is V(R = radius of earth). Column-I Column-II i. At a height h = R, value of E g p. decreases by a factor 1 4 ii. At a depth d = R 2 , value of E g q. decreases by a factor 1 2 iii. At a height h = R, value of V r. increases by a factor 11 8 iv. At a depth d = R 2 , value of V s. increases by a factor 2 t. decreases by a factor 11 8 Match the given columns and select the correct option from the codes given below. Codes
A satellite is moving in a circular orbit of radius r around earth with kinetic energy K. What work is to be done on the satellite to stop the satellite at any position in its orbit
Two stars each of mass M and radius R are approaching each other for a head-on collision. They start approaching each other when their separation is r >> R. If their speeds at this separation are negligible, the speed v with which they collide would be
If both the mass and the radius of earth decrease by 2%, the escape velocity from the surface of earth will
At what height above the surface of earth does the acceleration due to gravity become 36% of its value on the surface of earth if radius of earth is 6400 km?
Consider two satellites A and B. Both move around the earth in the same orbit but the mass of B is twice that of the mass of A.
The satellites orbiting the earth, eventually fall to the earth when they are left unsupervised or unattended because
Which graph correctly presents the variation of acceleration due to gravity with distance from the centre of the earth?
Mass of moon is 7.34 x 10 22 kg. If the acceleration due to gravity on the moon is 1.4 m / s 2 , the radius of the moon is (G = 6 . 667 × 10 – 11 Nm 2 / kg 2 )
The depth at which the effective value of acceleration due to gravity is g 4 is (R = radius of the earth)
Two masses m 1 and m 2 are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separatation of d is
The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)
The depth d at which the value of acceleration due to gravity becomes 1 n times the value at the surface, is [R =radius of the earth]
Assuming earth to be a sphere of a uniform density what is the value of gravitational acceleration in a mine 100 km below the earth’s surface (Given R = 6400 km)
The acceleration due to gravity at the poles and the equator is g p and g e respectively. If the earth is a sphere of radius R E and rotating about its axis with angular speed ω , then g p – g e is given by
The satellites orbiting the earth, eventually fall to the earth when they are left unsupervised or unattended because
If the net external force acting on a system of particles interacting through gravitational force is zero,
A body of weight 72N moves from the surface of earth at a height half of the radius of the earth, then gravitational force exerted on it will be :
A tunnel is dug along a diameter of earth of mass M e and radius R e . Force on a particle of mass ‘m’ placed in the tunnel at a distance ‘r’ from the centre is :
A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F 1 on a particle placed at a distance 2R from the centre of the sphere. A spherical cavity of radius (R/2) is now made in the sphere as shown in Figure. The sphere with the cavity now applies a gravitational force F 2 on the same particle. The ratio (F 2 /F 1 ) is :
Two particles of masses m 1 and m 2 , m 1 > m 2 move in circular paths under the action of their gravitational attraction. While doing so, their separation remains constant and equals ‘r’ . Radius of circular path of m 2 is:
Three particles, each of mass M are moving in a circle under their mutual gravitational forces such that they always form an equilateral triangle of side a while rotating. time period of motion of any particle is :
Figure shows two concentric spherical shells of masses M 1 and M 2 and of radii R 1 and R 2 , respectively. gravitational intensity at a distance x from the centre such that x > R 2 is :
Dependence of intensity of gravitational field (E) of earth with distance ( r) from center of earth is correctly represented by :
A spherical shell is cut into two pieces along a chord as shown in Figure. For points P and Q:
The period of a satellite in a circular orbit around a planet is independent of
When the body is moving up, the acceleration due to gravity will be :
As we go from the equator to the poles, the value of g :
The value of g at a particular point is 9.8 m/s 2 . Suppose the earth suddenly shrinks uniformly to half of its present size without losing any mass. The value of ‘g’ at the same point (assuming that the distance of the point from the centre of the earth does not shrink) will now be :
A planet has twice the values of mass and radius of earth. Acceleration due to gravity on the surface of the planet is :
If the radius of earth were to shrink by 1%, its mass remaining the same, the acceleration due to gravity on the earth’s surface would :
Two planets have radii R 1 and R 2 and densities d 1 and d 2 respectively. The ratio of the acceleration due to gravity on them will be :
A body weighing 20 kg on the surface of the earth is taken to a place 6000 km below the earth’s surface. Assuming the earth’s radius to be 6000 km, the weight lf the body at that depth is :
The radius of earth is 6400km and g = 9.8 m/sec 2 . If the body placed at the equator has to become weightless the earth should make one complete rotation in :
If earth is supposed to be a sphere of radius R, if g 30 is value of acceleration due to gravity at latitude of 30o and g at the equator. The value of ( g = g 36 ) is :
The ratio g g h , where g and g 1 , arc the accelerations due to gravity at the surface of the earth and at a height h above the earth’s surface respectively, is :
Average density of the earth :
The density of earth in terms of acceleration due to gravity (g), radius of earth (R) and universal gravitational constant (G) is :
The height at which the acceleration due to gravity becomes g 9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth is
When a body is taken from poles to equator on the earth, its weight :
Imagine a new planet having the same density as that of earth but it is three times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g’, then :
The dependence of acceleration due to gravity ‘g’ on the distance ‘r’ from the centre of the earth, assumed to be a sphere of radius R of uniform density B as shown in figure given ahead :
At what depth below the surface of earth, the value of g is the same as that at a height of 5 km?
The height at which the weight of a body become 1 16 th , its weight on the surface of earth (radius R) is :
At what height from the surface of earth the. gravitation potential an the value of g are – 5.4x 107 J kg -1 and 6.0 ms -2 respectively? Take the radius of earth as 6400 km.
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then
A particle of mass 10g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the. sphere : (you may take g = 6.67 x 10 -11 Nm 2 /kg 2 )
A body of mass m is released from a height equal to the radius R of the earth. What will be the velocity of the body when it strikes the surface of the earth?
A body of mass m is placed on earth surface which is taken from earth surface to a height of h = 3R, then change in gravitational potential energy is :
A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is :
The kinetic energy needed to project a body of mass m from the earth’s surface (radius R ) to infinity is
Energy required to move a body of mass m from an orbit of radius 2R to 3R is :
A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g 0 , the value of acceleration due to gravity at the earth’s surface, is :
The escape velocity from a planet of mass M and radius R is given by :
The ratio of the radius of earth to that of the moon is 10. The ratio of acceleration due to gravity on the earth and on the moon is 6. The ratio of the escape velocity from the earth’s surface to that from the moon is :
Escape velocity of a projectile from the surface of earth is about :
Escape velocity of a body from earth is about 11 km/sec. Assuming the mass and radius of the earth to be about 81 and 4 times the mass and radius of the moon, the escape velocity in km/sec from the surface of the moon will be :
The acceleration due to gravity on the surface of the moon is 1 6 that on the surface of earth and the diameter of the moon is one-fourth that of earth. The ratio of escape velocities on earth and moon will be :
An object is shot vertically upwards from the surface of earth with a speed nv e where v e is the escape speed and n< 1. If R is the radius of earth, maximum distance of the object from the center of earth will be :
The escape velocity for a rocket on earth is 11.2 km/sec. Its value on a planet where acceleration due to gravity is double that on the earth and diameter ofthe planet is twice that of the earth will be in km/sec :
The escape velocity from the earth is about 11 km/sec. The escape velocity from a planet having twice the radius and the same mean density as the earth is :
A projectile is fired with a speed v = 2 gR from the surface of earth. It escapes the gravitational pull of earth. Its speed in interstellar space will be :
A projectile is fired with a speed less than the escape speed. Its mechanical energy is :
Escape speed of a projectile that is fired vertically upward is v e . Another projectile has to be fired at 60° with the horizontal. Escape speed for this projectile will be :
A body is projected up from the surface of the earth with a velocity equal to 3/4 th of its escape velocity. If R be the radius of earth, the height it reaches is :
The escape velocity of 10 g body from the earth is 11.2 kms -1 . Ignoring air resistance, the escape velocity of 10 kg of the iron ball from the earth will be
For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth, then escape velocity for this planet will be :
The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv, where v is the escape velocity from the surface of the earth. The value of f is :
If v e is escape velocity and v o is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by :
A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 x 10 24 kg) have to be compressed to be a black hole
The ratio of escape velocity at earth (v e ) to the escape velocity at a planet (v p ) whose radius and mean density are twice as that of earth is :
A simple pendulum has a time period T 1 when on the earth’s surface and T 2 when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T 2 /T 1 is:
Two spherical stars each of mass M with their centres distant D apart revolve under mutual gravitational attraction about the point midway between their centres. The period of revolution will be :
A satellite is revolving around the earth in a circular orbit whose radius is R; work done by gravitational force in one revolution is :
The earth moves in an elliptical orbit with the sun ,S at one of foci as show in figure. Its rotational kinetic energy is maximum at the point :
A roller coaster is designed such that riders experience “weightlessness” as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between :
A particle is thrown with escape velocity v e =11.2km/s from the surface of earth. Its velocity at height 3R = 19200 Km is:
Energy required to transfer a 400 kg satellite in a circular orbit of radius 2R to a circular orbit of radius R, where R is the radius of the earth : [Given : g = 9.8 ms -2 ,R = 6.4 x 10 6 m]
For central force field : (1) Torque is zero about the central force field. (2) Angular momentum is conserved about any point in central force field. (3) Force is position dependent. (4) Force is conservative.
Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth. If the ratio of densities of earth ρ e and moon ρ m is ρ e ρ m = 5 3 then radius of moon R m in terms of R e will be
If R is radius of earth then the height above earth surface at which acceleration due to gravity reduces by 75% of its value on earth surface :
The period of moon’s rotation around the earth is nearly 29 days. If moon’s mass were 2 fold its present value and all other things remain unchanged, the period of moon’s rotation would be nearly (in days)
Two identical spheres each of radius R are placed with their centres at a distance nR, where n is integer greater than 2. The gravitational force between them will be proportional to
If g on the surface of the earth is 9.8 m/s 2 , its value at a height of 6400 km is (Radius of the earth = 6400km).
In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be (g = 10 ms -2 and radius of earth is 6400 kms)
A simple pendulum has a time period T 1 when on the earth’s surface and T 2 when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T 2 /T 1 is
A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth’s surface would
A body of mass m is taken from earth surface to the height h equal to radius of earth, the increase in potential energy will be
An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy E 0 . Its potential energy is
Two bodies of masses m 1 and m 2 are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is
A projectile is projected with velocity kv e in vertically upward direction from the ground into the space. ( v e is escape velocity and k < 1) . If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
The diagram showing the variation of gravitational potential of earth with distance from the centre of earth is
By which curve will the variation of gravitational potential of a hollow sphere of radius R with distance be depicted
A sphere of mass M and radius R 2 has a concentric cavity of radius R 1 as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as ( 0 ≤ r ≤ ∞ )
Which one of the following graphs represents correctly the variation of the gravitational field (F) with the distance (r) from the centre of a spherical shell of mass M and radius a
The curves for potential energy (U) and kinetic energy (E k ) of a two particle system are shown in figure. At what points the system will be bound?
The masses, each of mass m are kept on the vertices of an equilateral triangle of side a. Find the work needed to be done to change the length of the triangle twice of its original value.
A shell of mass M and radius R has a point mass m placed at a distance r from its centre. The gravitational potential energy U (r) vs r will be
A solid sphere of mass M and radius R has a spherical cavity of radius R /2 such that the centre of cavity is at a distance R /2 from the centre of the sphere. A point mass m is placed inside the cavity at a distance R /4 from the centre of sphere. The gravitational force on mass m is
The ratio of escape velocity on earth ( ν e ) to the escape velocity on a planet ( ν p ) whose radius and mean density are twice as that of earth is [NEET 2016]
Average density of the earth
The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and i are much smaller than the radius of the earth, then which of the following is correct ?
If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is
Two spherical bodies of the mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45. with the vertical, the escape velocity will be
The escape velocity of a body on the surface of the earth is 11.2 km./s. If the earth’s mass increases to twice its present value and radius of the earth becomes half, the escape velocity becomes
An extremely small and dense neutron star of mass M, and radius. R is rotating at an angular frequency ω . If an object is placed at its equator, it will remain stuck to it due to gravity if
The distance between the sun and the earth is r and the earth takes time t to make one complete revolution around the sun. Assuming the orbit of the earth around the sun to be circular, the mass of the sun will be proportional to
The escape velocity on the surface of the earth is 11.2 km/s. If mass and radius of a planet is 4 and 2 times respectively than that of earth, what is the escape velocity from the planet ?
A body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity. If fi is the radius of the earth, the maximum height attained by the body is
The ratio of the radii of the planets P 1 , and P 2 , is k. The ratio of the acceleration due to gravity is r. The ratio of the escape velocities from them will be
Suppose the gravitational force varies inversely as the nth power of the distance. Then, the time period of a planet in circular orbit of radius fi around the sun will be proportional to
An artificial satellite is moving in a circular orbit around the earth with a speed equal to the half of the escape velocity from the earth of radius r. The height of the satellite above the surface of the earth is
An artificial satellite is moving in a circular orbit around the earth at a height fi from the surface of the earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the earth, the speed with which it will hit the surface of the earth will be
Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is
A body starts from rest from a point distance R o from the centre of the earth. The velocity acquired by the body when it reaches the surface oft he earth will be (fire presents radius of the earth)
A satellite of mass m is orbiting the earth at a height H from its surface. If M be the mass of earth and R, its radius, then the energy required to pull the satellite from earth’s gravitational field will be
The escape velocity from the earth’s surface is 11 km,/sec. A certain planet has a radius twice that of the earth but its mean density is the same as that of the earth. The value of the escape velocity from this planet would be
A body of mass m rises to height h =R/ 5 from the earth’s surface, where R is earth’s radius. If g is acceleration due to gravity at earth’s surface, the increase in potential energy is
The gravitational potential energy of a rocket of mass 100 kg at a distance 10 7 m from the earth’s mass is 4.8 x 10 9 joule. The weight of the rocket in newton at a distance 10 9 m is
A geo-stationary satellite is orbiting the earth at a height at a above the surface of the earth, R being the radius of the earth. The time period of another satellite at a height of 2.5R from the surface of earth is
A ball of mass m is fired vertically upward from the surface of the earth with velocity nv e where v e is the escape velocity and n < 1. Neglecting air resistance, to what height will the ball rise ? Take radius of the earth as R
Two bodies of masses m 1 and m 2 , are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is
U the gravitational force is proportional to 1/ R 3 , the square of time period of revolution is proportional to
A mass m is placed in the cavity inside a hollow sphere of mass M as shown in fig. What is the gravitational force on the mass m ?
A spherical shell is cut into two pieces along a chord as shown in fig. P is a point on the plane of the chord. The gravitational field at P due to the upper part is I 1 ,and that due to lower part is I 2 . What is the relation between I 1 , and I 2 , ?
Two concentric shells of masses M 1 and M 2 , are . having radii r 1 , andr 2 . Which of the following is correct expression for the gravitational field on a mass m?
A solid sphere of uniform density and mass M has radius 4 m. Its centre is at the origin of the coordinate system. Two spheres of radii 1 m are taken out so that their centres are P (0, -2,0) and Q (0,2,0) respectively as shown in fig This leaves two spherical cavities. What is the gravitational field at the origin of the coordinate axis ?
A rocket is launched vertically from the surface of the earth of radius fi with an initial speed v. If atmospheric resistance is neglected, the maximum height h attained by the rocket is given by
Four particles of equal mass M move along a circle of radius .R under the action of their mutual gravitational attraction [Fig.]. The speed of each particle is
The variation of acceleration due to gravity as one moves away from earth’s centre is given by the graph
A body of mass M is taken from the surface of the earth to a height equal to the radius fi of the earth. The change in gravitational potential energy is
What is the weight of a body at a distance 2r from the centre of the earth if the gravitational potential energy of the body at a distance r from the centre of the earth is U
The mass of the earth is 81 times that of the moon and the radius of the earth is 3 5 times that of the moon’ The ratio of the escape velocity on the surface of earth to that on the surface of moon will be
Mass of moon is (1/81) times that of earth and its radius is (1/4) as the radius of the earth’ If the value of escape velocity at the surface of earth is 11 ‘ 2 km,/sec, its value at the surface of moon is
A body is projected upwards with a velocity of 4 x 11.2km / s from the surface of earth. What will be the velocity of the body when it escapes the gravitational pull of earth ?
The ratio of the radii of the planets P 1 and P 2 , is K 1 . The ratio of the acceleration due to the gravity on them is K 2 The ratio of the escape velocities from them will be
A bodyweighs 72 Non the surface of the earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface ?
The gravitational potential energy of a body of mass m at the earth’s surface is -mg R e .Its gravitational potential energy at a height R e from the earth’s surface will be (R =radius of the earth)
Two particles each of mass m are placed at points A and C such that AB =BC =L as shown in fig. The gravitational force on a third particle placed at D at a distance I metre on the perpendicular bisector of the line AC, is
Three point masses each of mass m are at the corners of an equilateral triangle of side L. The system rotates about the centre of the triangle with the separation of masses not changing during rotation. If T be the time period of rotation, then
Knowing that mass of moon is M/87, where M is the mass of tie earth, find the distance of the point from the moon, where gravitational field due to earth and moon cancel each other. Given that distance between earth and moon is 60 R, where R is the radius of earth
A simple pendulum has a time period T 1 , when on the earth’s surface and T 2 , when taken to a height R above the earth’s surface, where .R is the radius of the earth. The value of T 2 /T 1 , is
A body attains a height equal to the radius of the earth. The velocity of the body with which it was projected is
The acceleration due to gravity on the planet A is 9 times the acceleration due to the gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B
A satellite with kinetic energy E is revolving round the earth in a circular orbit. The minimum additional kinetic energy required for it to eecape into outer space is
The length of seconds pendulum is 1 m on earth. If mass and diameter of the planet are doubled than that of earth, then length becomes
Imagine a new planet having the same density as that of earth but it is 3 times bigger than the size of the earth. If acceleration due to gravity on the surface of the earth is g and that on the surface of the new planet is g’, then
A spacecraft of mass m describes a circular orbit of radius r 1 , around the earth of mass M. Calculate the additional energy to be imparted to the spacecraft to transfer it to a circular orbit of larger radius r 2 ,
