Q. Two spherical bodies of masses $M$ and $5M$ in free space with initial separation between their centres equal to 12$R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
A) 2.5 $R$
B) 4.5 $R$
C) 7.5 $R$
D) 1.5 $R$
Explanation
(c) Distance between the centre of spheres = 12$R$
$\therefore$ Distance between their surfaces =12$R - (2R + R) = 9R$
Since there is no external force, hence centre of mass must remain unchanged and hence
$\Rightarrow \ \ m_{1}r_{1} = m_{2}r_{2} \Rightarrow Mx = 5M(9R - x) \Rightarrow x = 7.5R$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.