Question

Two spherical bodies of mass M and 5 M and radii R and 2R respectively 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 just before collision is :

• A. 1.5 R
• B. 2.5 R
• C. 4.5 R
• D. 7.5 R

Answer 1

Answer: (D)

7.5 R

Answer 2

As the spherical bodies have their own size so the distance covered by both the body 12R-3R=9R, but individual distance covered by each body depends upon their masses.

We know that bodies are moving under the effect of mutual attraction only, so their position of centre of mass remains unaffected. Let smaller body covers distance x just before collision from, m1r1 = m2r2

Þ M x = 5 M (9R–x) Þ x = 7.5 R