{"id":13569,"date":"2022-01-25T12:08:10","date_gmt":"2022-01-25T06:38:10","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=13569"},"modified":"2025-05-29T10:27:28","modified_gmt":"2025-05-29T04:57:28","slug":"jee-main-physics-center-of-mass-momentum-and-impulse-previous-year-questions-with-solutions","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/jee-main\/physics\/jee-main-physics-center-of-mass-momentum-and-impulse-previous-year-questions-with-solutions\/","title":{"rendered":"JEE Main Physics Center of Mass, Momentum and Impulse Previous Year Questions with Solutions"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/jee-main\/physics\/jee-main-physics-center-of-mass-momentum-and-impulse-previous-year-questions-with-solutions\/#JEE_Main_Physics_Center_of_Mass_Momentum_and_Impulse_Previous_Year_Questions_with_Solutions\" title=\"JEE Main Physics Center of Mass, Momentum and Impulse Previous Year Questions with Solutions\">JEE Main Physics Center of Mass, Momentum and Impulse Previous Year Questions with Solutions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/jee-main\/physics\/jee-main-physics-center-of-mass-momentum-and-impulse-previous-year-questions-with-solutions\/#JEE_Foundation_Class_for_10\" title=\"JEE Foundation Class for 10\">JEE Foundation Class for 10<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/jee-main\/physics\/jee-main-physics-center-of-mass-momentum-and-impulse-previous-year-questions-with-solutions\/#JEE_Foundation_Class_for_9\" title=\"JEE Foundation Class for 9\">JEE Foundation Class for 9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/jee-main\/physics\/jee-main-physics-center-of-mass-momentum-and-impulse-previous-year-questions-with-solutions\/#Subjective_Numerical_integer_type\" title=\" Subjective \/ Numerical integer type\"> Subjective \/ Numerical integer type<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"JEE_Main_Physics_Center_of_Mass_Momentum_and_Impulse_Previous_Year_Questions_with_Solutions\"><\/span>JEE Main Physics Center of Mass, Momentum and Impulse Previous Year Questions with Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For JEE Main other Engineering Entrance Exam Preparation,  <strong>JEE Main Physics Center of Mass, Momentum and Impulse<\/strong> Previous Year Questions with Solutions is given below.<\/p>\n<p><span style=\"color: #0000ff;\"><strong>Multiple Choice with ONE correct answer:<\/strong><\/span><\/p>\n<p><strong>1.Two particles A and B, initially at rest, move to\u00ad wards each other under mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, the speed of the centre of mass of the system is    [1982-3 marks]<\/strong><\/p>\n<p><strong>a) 3v             b) v                    <\/strong><\/p>\n<p><strong> c) 1.5v          d) zero<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans: <span style=\"color: #0000ff;\">d<\/span><\/strong><\/span><\/p>\n<p><strong>2.An isolated particle of mass m is moving in horizontal plane (x-y) along the x-axis at a certain height above the ground. It suddenly explodes into two fragments of masses m\/4 and 3m\/4. An instant later, the smaller fragment is at y = + 15 cm. The larger fragment at this instant is at [1997-1 mark]<\/strong><\/p>\n<p><strong>a) y = \u2013 5cm                  b) y = + 20cm              <\/strong><\/p>\n<p><strong>   c) y = + 5cm              d) y = \u2013 20cm<\/strong><\/p>\n<p><strong><span style=\"color: #0000ff;\">Ans:a<\/span><\/strong><\/p>\n<p style=\"text-align: left;\"><strong>3.Two particles of masses m<sub>t<\/sub> and m<sub>2<\/sub>, in projectile motions have velocities v<sub>t<\/sub> &lt; v<sub>2<\/sub> respectively at time t=0. They collide at time t<sub>0<\/sub>. Their velocities become v, and v<sub>2<\/sub> at time 2t<sub>0<\/sub> while moving in air. The value of<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/24641186693_551f82f60e_o.png\" alt=\"3q1\" width=\"344\" height=\"55\" \/><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:c<\/strong><\/span><\/p>\n<div class=\"card\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-10\"><br \/>\n<noscript><img style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/09\/Screenshot-2024-08-28-114053-e1724825703440.jpg\" alt=\"JEE Foundation Class 10 Online Course\" data-eio=\"l\" \/><\/noscript><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-10\"><img loading=\"lazy\" class=\" lazyloaded alignnone\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/09\/Screenshot-2024-08-28-114053-e1724825703440.jpg\" alt=\"jee-foundation-course-for-class-10\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/09\/Screenshot-2024-08-28-114053-e1724825703440.jpg\" \/><\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"JEE_Foundation_Class_for_10\"><\/span>JEE Foundation Class for 10<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: center;\">JEE Foundation Class for 10 enhances critical thinking and problem-solving skills through engaging activities and advanced learning techniques, ensuring academic excellence.<br \/>\n<a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-10\"><button><strong>JEE Foundation Class for 10<\/strong><\/button><\/a><\/p>\n<\/div>\n<p><strong>4.Two blocks of masses 10 kg and 4 kg are con\u00adnected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m\/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is :      [2002]<\/strong><\/p>\n<p><strong>a) 30 m\/s                   b) 20 m\/s   <\/strong><\/p>\n<p><strong>c) 10 m\/s                    d) 5 m\/s<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:c<\/strong><\/span><\/p>\n<p><strong>5.Two small particles of equal masses start moving in opposite directions from a point A in a horzontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A? [2009]<\/strong><\/p>\n<p><strong>a) 4                      b) 3 <\/strong><\/p>\n<p><strong>c) 2                       d) 1<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:c<\/strong><\/span><\/p>\n<p><strong>6.Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are; outer circle (0,0), left inner circle (-a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, -a). The y-corrdinate of the centre of mass of the ink in this drawing is [2009]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:a<\/strong><\/span><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Multiple Choice with ONE or MORE THAN ONE correct answers<\/strong><\/span><\/p>\n<p><strong>7. A ball hits the floor and rebounds after an inelastic collision. In this case         [1986-2 marks]<\/strong><\/p>\n<p><strong>(a)the momentum of the ball just after the collision is the same as that just before the collision<\/strong><br \/>\n<strong>(b)the mechanical energy of the ball remains the same in the collision<\/strong><br \/>\n<strong>(c)the total momentum of the ball and the earth is conserved<\/strong><br \/>\n<strong>(d)the total energy of the ball and the earth is conserved.<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:c,d<\/strong><\/span><\/p>\n<p><strong>8.A shell is fired from a cannon with a velocity v (m\/sec) at an angle 0 with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces \u2018 retraces its path to the cannon and the speed (in m\/sec) of the other piece immediately after the explosion is         [1986-2 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:a<\/strong><\/span><\/p>\n<p><strong>9.A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal with speed 2v and v respectively, strike the bar [as shown in the fig.] and stick to the bar after collision.  Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by co,E and v<sub>c <\/sub>respectively, we have after collision.   [1991-2 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:a,c,d<\/strong><\/span><\/p>\n<div class=\"card\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-9\"><br \/>\n<noscript><img style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/09\/Screenshot-2024-08-28-114053-e1724825703440.jpg\" alt=\"JEE Foundation Class 9 Online Course\" data-eio=\"l\" \/><\/noscript><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-9\"><img loading=\"lazy\" class=\" lazyloaded alignnone\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/09\/Screenshot-2024-08-28-114053-e1724825703440.jpg\" alt=\"jee-foundation-course-for-class-9\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/09\/Screenshot-2024-08-28-114053-e1724825703440.jpg\" \/><\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"JEE_Foundation_Class_for_9\"><\/span>JEE Foundation Class for 9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: center;\">JEE Foundation Class for 9 enhances critical thinking and problem-solving skills through engaging activities and advanced learning techniques, ensuring academic excellence.<br \/>\n<a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-9\"><button><strong>JEE Foundation Class for 9<\/strong><\/button><\/a><\/p>\n<\/div>\n<p><strong>10.Two blocks A and B, each of mass m, are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B, and collides elastically with A. Then. [1993-2 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:b,d<\/strong><\/span><br \/>\n<strong>11.Two balls, having linear momenta p<sub>t<\/sub> = pi and p<sub>2<\/sub> = -pi, undergo a collision in free space. There is no external force acting on the balls. Let P<sup>1<\/sup> and P<sub>2<\/sub> be their final momenta. The following option(s) is are NOT ALLOWED for any non-zero value of p,a<sub>1<\/sub>,a<sub>2<\/sub>,b<sub>1<\/sub>,b<sub>2<\/sub>,c<sub>1<\/sub> and c<sub>2<\/sub>    [2008]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:a,d<\/strong><\/span><\/p>\n<p><strong>12.A point mass of 1 kg collides elastically with a stationary point ipass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms<sup>4<\/sup>. Which of the following statements(s) (are) correct for the system of these two masses ?<\/strong><\/p>\n<p><strong>(a)Total momentum of the system is 3 kg ms<sup>-1<\/sup><\/strong><br \/>\n<strong>(b)Momentum of 5kg mass after collision is 4kg ms<sup>-1<\/sup><\/strong><br \/>\n<strong>(c)Kinetic energy of the centre of mass is 0.75 J<\/strong><br \/>\n<strong>(d)Total kinetic energy of the system is 4 J<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:a,c<\/strong><\/span><\/p>\n<p><span style=\"color: #0000ff;\"><strong>H Assertion &amp; Reasoning type Instructions :<\/strong><\/span><br \/>\n<span style=\"color: #0000ff;\"><strong> Each question contains statement-1 (assertion) and statement-2 (reason). Of these statements, mark correct choice if<\/strong><\/span><\/p>\n<p><strong>13.Statement-1 ;If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.<\/strong><br \/>\n<strong> Statement-2 :The linear momentum of an isolated system remains constant.     [2007-3 marks]<\/strong><\/p>\n<p><strong>(a).Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1<\/strong><br \/>\n<strong> (b).Statements-1 and 2 are true and statement-2 is not a correct explanation for statement-1<\/strong><br \/>\n<strong> (c).Statement-1 is true, statement-2 is Base<\/strong><br \/>\n<strong> (d).Statement-1 is false, statement-2 is true.<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:d<\/strong><\/span><\/p>\n<p><strong>14.Statement -1 In an elastic collision between two bodies, the relative speed of the bodies after colision is equal to the relative speed before the collision<\/strong><br \/>\n<strong> because<\/strong><br \/>\n<strong> Statement -2 In an elastic collision, the linear momentum of the system is conserved * [2009-3 marks]<\/strong><\/p>\n<p><strong>(a).Statement -1 is True, Statement -2 is True; Statement-2 is a correct explanation for Statement-1<\/strong><br \/>\n<strong> (b).Statement -1 is True, Statement -2 is True; Statement-2 is not a correct explanation for Statement-1<\/strong><br \/>\n<strong> (c).Statement -1 is True, Statement -2 is False<\/strong><br \/>\n<strong> (d).Statement -1 is False, Statement -2 is True<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:b<\/strong><\/span><\/p>\n<h3><span style=\"color: #0000ff;\"><strong> Subjective \/ Numerical integer type<\/strong><\/span><\/h3>\n<p><strong>15.A body of mass m moving with a velocity v in the x-direction collides with another body of mass M moving in the y-direction with a velocity V. They coalese into one body during collision. Find.<\/strong><\/p>\n<p><strong>(a)The direction and magnitude of the momentum of the composite body,<\/strong><br \/>\n<strong> (b)The fraction of the initial kinetic energy transformed into heat during the collision          [1978]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:<\/strong><\/span><\/p>\n<p><strong>16.When a ball is thrown up, the magnitude of its momentum decreases and then increases. Does this violate the conservation of momentum principle?  [1979]<\/strong><\/p>\n<p><strong><span style=\"color: #0000ff;\">Ans :No<\/span><\/strong><\/p>\n<p><strong>17.A 20g bullet pierces through a plate of mass Mplkg and then comes to rest inside a second plate of mass M<sub>2<\/sub> = 2.98 kg as shown in the figure. It is found that the two plates initially at rest, now move with equal velocities. Find the percentage loss in the initial velocity of the bullet when it is between Mj and M<sub>2<\/sub>. Neglect any loss of material of the plates due to the action of bullet. [1979]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:25%<\/strong><\/span><\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td style=\"text-align: center;\" colspan=\"2\"><strong>JEE Online Courses &amp; Study Materials<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-9\"><strong>JEE Foundation Class 9 Online Course<\/strong><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/jee-foundation-course-for-class-10\"><strong>JEE Foundation Class 10 Online Course<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/jee-class-11-online-course\"><strong>JEE Class 11 Online Course<\/strong><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-jee-main-prep\"><strong>One Stop Solution for JEE Prep<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><strong>18.A circular plate of uniform thickness has a diameter of 56cm. A circular portion of diameter 42cm is removed from one edge of the plate as shown in the figure. Find the position of the centre of mass of the remaining portion                                                                                                                             [1980]<\/strong><\/p>\n<p><strong><span style=\"color: #0000ff;\">Ans:9 cm to left of centre of bigger circle<\/span><\/strong><br \/>\n<strong>19.A body of mass 1kg, initially at rest, explodes and breaks into three fragments of masses in the ratio 1:1:3. The two pieces of equal mass fly off per\u00adpendicular to each other with a speed of 30 m\/sec each. What is the velocity of the heavier fragment? [1981-3 marks]<\/strong><\/p>\n<p><strong><span style=\"color: #0000ff;\">Ans: 10\u221a2m\/s<\/span><\/strong><\/p>\n<p><strong>20.Three particles A,B and C of equal mass move with equal speed v along the medians of an equilateral traingle as shown in fig. They collide at the cen\u00adtroid of the traignle. After the collision, A comes to rest, B retraces its path with the speed v. What is the velocity of C ?        (1982-2Marks)<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:  v\u2019= v = velocity of C<\/strong><\/span><\/p>\n<p><strong>21.A block of mass M, with a semicircular track of radius R, rests on a horizontal frictionless surface. A uniform cylinder of radius r and mass m is re\u00adleased from rest at the top point A, as shown in figure. The cylinder slips on the semicircular fric\u00adtionless track. How far has the block moved when the cylinder reaches the bottom (point B) of the track? How fast is the block moving when the cyl\u00adinder reaches the bottom of the track?        [1983-7 marks]<\/strong><\/p>\n<p><strong>22.Two bodies A and B of masses m and 2m respectively are placed on a smooth floor. They are connected by a spring  A third body C of mass m moves with velocity v<sub>0<\/sub> along the line joining A and B and collides elastically with A as shown in fig. At a certain instant \u2018 of time t<sub>0<\/sub> after collision, it is found that the instantaneous velocities of A and B are the same. Further at this instant the compression of the spring is found to be jc<sub>0<\/sub> . Determine<\/strong><br \/>\n<strong> i) the common velocity of A and B at time t<sub>0<\/sub> and<\/strong><br \/>\n<strong> ii) the spring constant.<\/strong><\/p>\n<p><strong>23.A ball of mass lOOg is projected vertically upwards from the ground with a velocity of 49m\/sec. At the same time another identical ball is dropped from a height of 98m to fall freely along the same path as that followed by the first ball. After some time the two balls collide and stick together and finally fall to the ground. Find the time of flight of the masses. [1985-8 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:6.53sec<\/strong><\/span><strong>24.A simple pendulum is suspended from a peg on a vertical wall. The pendulum is pulled away from the wall to a horizontal position (sec fig.) and released. The ball hits the wall the co-efficient of restituion being  2\u2044 \u221a5   What is the minimum number of collisions after which theamplitude of oscillations becomes less than 60 degree?                     [1987-7 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:4<\/strong><\/span><\/p>\n<p><strong>25.A bullet of mass M is fired with a velocity 50 m\/s at an angle 0with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass 3M suspended by a massless string of length (10\/3)metre and gets embedded in the bob, After the collision, the string moves through an angle of 120\u00b0. Find<\/strong><br \/>\n<strong> i)the angle 0;<\/strong><br \/>\n<strong> ii)the vertical and horizontal coordinates of the initial position of the bob with respect to the point of firing of the bullet. Take g = 9.8m\/s<sup>2                                                 <\/sup>[1988-6 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:  (i)\u03b8=47\u00b0     (ii):   46cm, 122.6cm<\/strong><\/span><\/p>\n<p><strong>26.A thin uniform bar lies on a frictionless horizontal surface and is free to move in any way on the surface. Its mass is 0.16kg and length \u221a3  metre. Two particles each of mass 0.08 kg, are moving on the same surface and towards the bar in a direction perpen\u00addicular to the bar, one with a velocity of lOm\/s, and other with 6m\/s as shown in fig. The first par\u00adticle strikes the bar at point A and the other at point B. Points A and B are at a distance of 0.5m from the centre of the bar. The particles strike the bar at the same instant of time and stick to the bar on collision. Calculate the loss of the kinetic energy of the system in the above collision process.  [1989-8 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:2072j<\/strong><\/span><\/p>\n<p><strong>27.An object\u2019of mass 5kg is projected with a velocity of 20m\/s at an angle of 60\u00b0 to the horizontal. At the highest point of its path the projectile explodes and breaks up into two fragments of masses 1kg and 4kg. The fragments separate horizontally after the explosion. The explosion releases internal energy such that the kinetic energy of the system at the highest point is doubled. Calculate the separation between the two fragments when they reach the ground.                           [1990-8 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:44.25m<\/strong><\/span><\/p>\n<p><strong>28.A block A of mass 2m is placed on another block B of mass 4m which in turn is placed on a fixed table. The two blocks have same length 4d and they are placed as shown in fig. The coefficient of friction (both static and kinetic) between the block B and table is |Li. There is no friction between the two blocks. A small object of mass m moving horizontally along a line passing through the centre of mass (COM), of the block B and perpendicular to its face with a speed v collides elastically with the block B at a height d above the table.   <\/strong><strong>[1991-8 marks]<\/strong><\/p>\n<p><strong>a)What is the minimum value of v(call it v<sub>0<\/sub>) required to make the block A topple ?<\/strong><br \/>\n<strong>b)If v = 2v<sub>0<\/sub>, find the distance (from the point P in the figure) at which the mass m falls on the table after collision. (Ignore the role of friction during the collision)<\/strong><\/p>\n<p><strong><span style=\"color: #0000ff;\">Ans:<\/span><\/strong><\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/25272245805_897cd306df_o.png\" alt=\"jee-main-previous-year-papers-questions-with-solutions-physics-centre-of-mass-momentum-impulse--28a\" width=\"166\" height=\"56\" \/><\/p>\n<p><strong> <\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/24974860920_60571e3ac7_o.png\" alt=\"jee-main-previous-year-papers-questions-with-solutions-physics-centre-of-mass-momentum-impulse-29q\" width=\"563\" height=\"405\" \/><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/24645509493_8b98e8b60a_o.png\" alt=\"jee-main-previous-year-papers-questions-with-solutions-physics-centre-of-mass-momentum-impulse-29a\" width=\"97\" height=\"31\" \/><\/strong><\/span><\/p>\n<p><strong>30.A uniform thin rod of mass M and length L is standing vertically, along the y-axis, on a smooth horizontal surface, with its lower end at the origin (0,0). A slight disturbance at t=0 causes the lower end to slip on the smooth surface along the positive x-axis and the rod starts falling<\/strong><\/p>\n<p><strong>i)What is the path, followed by the centre of mass of the rod, during its fall ?<\/strong><br \/>\n<strong> ii)Find the equation of the trajectory of a point on the rod, located at a distance r, from die lower end. What is the shape of the path of this point?    [1993-5+1 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans: (i): Stright line (ii): Ellipse<\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong>31.A small sphere of radius R is held against the inner surface of a larger sphere of radius 6R. The masses of large and small spheres are 4M and M respectively. This arrangement is placed on a horizontal table. There is no friction between any surfaces of contact. The small sphere is now released. Find the coordinates of the centre of the larger sphere when the smaller sphere reaches the other extreme position.    [1996-3 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:(L+2R,0)<\/strong><\/span><\/p>\n<p><strong>32.A cart is moving along +x direction with a velocityof 4m\/s. A person in the cart throws a stone with a velocity of 6m\/s relative to himself. In the frame of reference of the cart the stone is thrown in y-z plane making an angle of 30\u00b0 with the vertical z-axis. At the highest point of its trajectory, the stone hits an object of equal mass hung vertically from the branch of a tree by means of a string of length L. A completely inelastic collision occurs, in which the stone gets embedded in the object. Determine                                         [1997-5 marks]<\/strong><\/p>\n<p><strong>(a).the speed of the combined mass immediately after the collision with respect to an observer on the ground.<\/strong><\/p>\n<p><strong> (b).the length L of the string such that the tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:(I)2.5M\/S<\/strong><\/span><\/p>\n<p><span style=\"color: #0000ff;\"><strong>         (II)L=0.318m<\/strong><\/span><\/p>\n<p><strong>33.A wedge of mass m and triangular cross section (AB=BC=CA=2R) is moving with a constant velocity vi \u02c6  towards a sphere of radius R fixed on a smooth horizontal table, as shown in the figure. The wedge makes an elastic collision with the fixed sphere and returns along the same path,any rotation* Neglect all friction and suppose that the wedge remains in contact with the sphere for a very short time \u0394t during which the sphere exerts a constant force F\u203e on the wedge. [1998-8 marks]<\/strong><\/p>\n<p><strong>(a)Find the force p and also the normal force N exerted by the table on the wedge during the time \u0394t<\/strong><br \/>\n<strong> (b)Let h denote the perpendicular distance between the centre of mass of the wedge and the line of action of F\u00af. Find the magnitude of the torque due to the normal force n about the centre of the wedge dining the interval\u0394t <\/strong><\/p>\n<p><strong>34Two blocks of mass 2kg and M are at rest on an inclined plane and are separated by a distance of 6.0m as shown. The coefficient of friction between each of the blocks and the inclined plane is 0.25. The 2kg block is given a velocity of lO.Om\/s up the inclined plane. It collides with M, comes back and has a velocity of l.Om\/s when it reaches its initial position. The other block M after the collision moves 0.5m up and comes to rest. Calculate the coefficient of restitution between the blocks and the mass of the block M. [Take sin\u03b8 \u2248 tan\u03b8= 0.05 and g = 10m\/s<sup>2<\/sup>] [1999-10 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans: 0.84,  15.02kgs<\/strong><\/span><\/p>\n<p><strong>35.A rod AB of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits the end \u2018A\u2019 of the rod with a velocity v<sub>0<\/sub> in a direction perpen\u00addicular to AB. The collision is elastic. After the \u2018collision the particle comes to rest.     [2000-10 marks]<\/strong><\/p>\n<p><strong>(a)Find the ratio m\/M .<\/strong><br \/>\n<strong>(b)A point P on the rod is at rest immediately after the collision. Find the distance AP.<\/strong><br \/>\n<strong>(c)Find the linear speed of the point P after a time \u03c0L\/(3v<sub>0<\/sub>) after the collision.<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:m\/M=1\/4  , (b) AP=2L\/3 , (c)Vp=Vo\/2\u221a2<\/strong><\/span><\/p>\n<p><strong>36.A car P is moving with auniform speed of 5(3<sup>1\/2<\/sup>) m\/s towards a carriage of mass 9 Kg at rest kept on the rails at a point B as shown in fig. The height AC is 120 m. Cannon balls of 1 Kg are fired from the car with an initial velocity 100 m\/s at an angle 30\u00b0 with the horizontal. The first canon ball hits the stationary carriage after a time ^ and sticks to it. Determine t<sub>0<\/sub>. At t<sub>0<\/sub>, the second cannon ball is fired. Assume that the resistive force between the rails and the carriage is constant and ignore the vertical motion of the carriage throughout. If the second ball also hits and sticks to the carriage. What will be the horizontal velocity of the carriage just after the second impact?     [2001-10 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:to=12Seconds,15.75m\/s<\/strong><\/span><\/p>\n<p><strong>37.Two heavy metallic plates are joined together at 90\u00b0 to each other. A laminar sheet of mass 30 Kg is hinged at the line AB joining the two heavy metallic plates. The hinges are frictionless. The moment of inertia of the laminar sheet about an axis parallel to AB and passing through its centre of mass is 1.2 Kg-m<sup>2<\/sup>. Two rubber obstacles P and Q are fixed, one on each metallic plate at a distance 0.5 m from the line AB. This distance is chosen so that the reaction due to the hinges on the laminar sheet is zero during the impact. Initially the laminar sheet hits one of the obstacles with an angular velocity 1 rad\/s and turns back. If the impulse on the sheet due to each obstacle is 6 N-s<\/strong><br \/>\n<strong>[2001-10 marks]<\/strong><br \/>\n<strong>(a).Find the location of the centre of mass of the laminar sheet from AB.<\/strong><br \/>\n<strong> (b).At what angular velocity does the laminar sheet come back after the first impact?<\/strong><br \/>\n<strong> (c).After how many impacts, does the laminar sheet come to rest ?<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans: (a):0.1m , (b): 1rad\/sec , (c): Sheet swings Infinitly<\/strong><\/span><\/p>\n<p><strong>38.A particle\u2019 of mass m, moving in a circular path of radius R with a qpnstant speed v<sub>2<\/sub>is located at point (2R,0) at time t=0 and a man starts moving with a velocity V\u00b9 along the +ve y-axis from origin at time t=0. Calculate the linear momentum of the particle with respect to the man as a function of time.        [2003-2 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans: <\/strong><\/span><strong>39.Two masses m<sub>}<\/sub> and m<sub>2<\/sub> are connected by a light spring of natural length l<sub>0<\/sub> which is compressed completely and tied by a string. This system while moving with a velocity v<sub>0<\/sub> along +ve x-axis passes through the origin at t=0. At this position the string snaps. Position of mass m<sub>t<\/sub> at time t is given by the equation Xj (t) = v<sub>0<\/sub>t \u2013 A (l \u2013 cos cot) calculate[2003-4 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans: <\/strong><\/span><strong>(a).position of the particle as a function of time<\/strong><br \/>\n<strong> <sub><span style=\"font-size: 16px; line-height: 24px;\">(b)l<\/span>0 <\/sub>in terms of A.<\/strong><\/p>\n<p><strong>40.There is a rectangular plate of mass M kg of dimensions (a x b). The plate is held in horizontal position by striking n small balls, each of mass m, per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity v. What is v?   It is given<\/strong><br \/>\n<strong> n = 100, M = 3 kg, m = 0.01 kg; b = 2 m; a = 1m; g = 10 m\/s<sup>2<\/sup>.     [2006-6 marks]<\/strong><\/p>\n<p><strong><span style=\"color: #0000ff;\">Ans:10m\/s<\/span><\/strong><br \/>\n<span style=\"color: #000000;\"><strong> 41. Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m\/s and makes \u2018 an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m\/s) of the object C.            [2009]<\/strong><\/span><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:4<\/strong><\/span><\/p>\n<p><span style=\"color: #0000ff;\"><strong>True \/ False Type<\/strong><\/span><\/p>\n<p><strong>42.Two particles of mass 1kg and 3kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is 2m\/s, their centre of mass has a velocity of 0.5m\/s. When the relative velocity of approach becomes 3m\/s, the velocity of the centre of mass is 0.75m\/[1989-2 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:False<\/strong><\/span><\/p>\n<p><strong>43.A particle of mass 4m which is at rest explodes  into three fragments. Two of the fragments each of mass m are found to move with a speed v each in mutually perpendicular directions. The total energy released in the process of explosion is     [1987-2 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:3\/2mv\u00b2<\/strong><\/span><\/p>\n<p><strong><span style=\"color: #0000ff;\">Fill in the blanks typeV<\/span><\/strong><\/p>\n<p><strong>44.The magnitude of the force (in newton) acting on a body varies with time t (in microsecond) as shown in the fig. AB, BC and CD are straight line segments. The magnitude of the total impulse of the force on the body from t = 4\u03bcs to t = 16\u03bcs \u2026..     [1994-2 marks]<\/strong><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Ans:0.005<\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>JEE Main Physics Center of Mass, Momentum and Impulse Previous Year Questions with Solutions For JEE Main other Engineering Entrance [&hellip;]<\/p>\n","protected":false},"author":31,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"\"Get JEE Main Physics Center of Mass, Momentum and Impulse Previous Year Questions with Solutions on Infinity Learn.\"","custom_permalink":"jee-main\/physics\/jee-main-physics-center-of-mass-momentum-and-impulse-previous-year-questions-with-solutions\/"},"categories":[4],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>JEE Main Physics Center of Mass, Momentum and Impulse Previous Year Questions with Solutions - 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