Question

Two spherical bodies of masses m and $5$M and radii R and $2$R, respectively, are released 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

Answer 1

The correct option is C $7.5$R

ATQ, there is no external force acting on the system of two masses $m$ & $5m$.. Thus, this implies that center of mass will remain unchanged.

Let $m$ at $(0,0)$ & $5m$ at $(12R,0)$.

then,

$CO{M}_1=\frac{(0\times m)+(5m\times 12R)}{(m+5m)}=10R$

At the time of collision, the COM will be $3R$ apart from each other.

After collision,

$CO{M}_2=\frac{(m\times x)+5m(x+3R)}{6m}$

As, $CO{M}_1=CO{M}_2$

$\Rightarrow 10R=\frac{6mx+15mR}{6m}$

$\Rightarrow x=7.5R$

$\therefore$The distance covered by the smaller body just before collision is $7.5R$