Question

Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ 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. $4.5R$
• B. $7.5R$
• C. $1.5R$
• D. $2.5R$

Answer 1

The correct option is B $7.5R$



Let $x_1$ be distance moved by $M$ and
$x_2$ be distance moved by $5M$

As their C.M. will remain stationary
$\left(M\right)\left(x_1\right)=\left(5M\right)\left(x_2\right)$
$x_1=5x_2$

and

for touching
$x_1+x_2=9R$
$6x_2=9R\Rightarrow x_2=1.5R$
$\Rightarrow x_1=7.5R$