Question

# Two spherical bodies of mass M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is:

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

## The correct option is A 7.5RAssuming velocities of masses M and 5M are v1 and v2 respectivelyUsing conservation of momentum principleMv1+5Mv2=0⇒v2=−v15...(i)Using energy conservation principleΔP.E.=ΔK.E.The P.E. is given as Gm1m2r−G5M212R−(−G5M23R)=12Mv21+125Mv22−0from equation (i) substituting value of v215GM212R=12Mv21+125M(v15)2G5M24R=12Mv21+12Mv21512Mv21=K.E. of mass M just before collision =25GM224RUsing work energy theorem:work done by gravitational force =ΔK.E.∫r12RF.dr=12mv1∫r′12RGM5Mr2dr=12mv1[GM5Mr]r′12R=12mv1GM5M(1r−112R)=25GM224R⇒r=7.5Rhence correct answer is option A

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