Questions

A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F_{1} on a particle placed at

P, distance 2R from the centre O of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in figure. The sphere with cavity now applies an gravitational force F_{2} on same particle placed at P. The ratio F_{2}/ F_{1} will be

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a

1 /2

b

7/9

c

3

d

7

detailed solution

Correct option is B

Gravitational force due to solid sphere, F1=GMm(2R)2 where M and mare masses of the solid sphere and particle respectivelyand R is the radius of the sphere. The gravitational force on particle due to sphere with cavity = force due to solid sphere creating cavity, assumed to be present above at that position.i, e, F2=GMm4R2-G(M/8)m(3R/2)2=736GMmR2So, F2F1=7GMm36R2/GMm4R2=79

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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

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