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 centers equal to $12R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before the collision is

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

Answer 1

Answer: (B)

$7.5R$

We know that the center of mass will remain constant, taking origin at the center of sphere of mass $M$ and $x-axis$ to the left towards the sphere $5M$

$x=\frac{0\times M+5M\times 12R}{M+5M}$

$x=10R$

After collision

$\frac{mx+5M(x+3R)}{6m}=10R$

$6x+15R=60R$

$6x=45R$

$x=7.5R$