Question

Two spherical bodies of mass $M$ and $5M$ 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 the gravitational force only, then the distance covered by the smaller body just before collision is

• A. $7.5R$
• B. $7R$
• C. $6R$
• D. $8.5R$

Answer 1

The correct option is A $7.5R$

$m_1{x}_1=m_2{x}_2$

Given: $m_1=M,m_2=5M$

Initially when the system is at rest (i.e $v_{cm}=0$ and the net external force is zero, the location of centre of mass is fixed.

Let $x$ be distance travelled by smaller mass $M$, then distance travelled by bigger mass will be

$12R-(R+2R)-x=9R-x$

$Mx=5M(9R-x)$

$x=7.5R$

Final answer : (a)