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Question

Two spherical bodies of mass m, 5m and radius R, 2R respectively are released in free space with an initial separation of 12R between their centres. If they attract each other due to gravitational force alone, then the distance covered by the smaller body just before the collision is

A
2.5R
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B
4.5R
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C
7.5R
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D
1.5R
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Solution

The correct option is C 7.5R

Froms Newtons law of Gravitation,
F=Gm(5m)(12Rx)2=masmall=5mabigasmall=G(5m)(12Rx)2abig=G(m)(12Rx)2

From Equation of motion:
x=12asmallt2=12G(5m)(12Rx)2t2....(1)
9Rx=12abigt2=12G(m)(12Rx)2t2...(2)

(1)÷(2) x=7.5 R

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