Two spherical bodies have masses M and 5M and radii R and 2R. Initially the separation between their centres is 12R. They attract each other only by gravity. What distance does the smaller sphere move before the spheres collide?
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Question

Two spherical bodies have masses M and 5M and radii R and 2R. Initially the separation between their centres is 12R. They attract each other only by gravity. What distance does the smaller sphere move before the spheres collide?

Options

G1 Physics · Accepted Answer

Step 1: No external force acts, so centre of mass stays fixed. The centres move together by 12R−(R+2R)=9R before contact. Step 2: Their displacement ratio is xₘ/x₅ₘ=5; hence xₘ=5×9R/6=7.5R. Final answer: C — 7.5R.