Question

Two spherical bodies having masses $M$ and $3M$ and radii $r$ and $4r$ respectively are released in free space rest such that the initial separation between their centres is $13r$. If only force is gravitational attraction distance covered by the smaller body just before collision is.

• A. $6r$
• B. $2r$
• C. $\frac{9}{4r}$
• D. $\frac{39r}{4}$

Answer 1

The correct option is C $\frac{9}{4r}$

The center of mass of the 2 body system will not be changed because there is no external force acting on the system.

Let mass M be initially at origin. Centre of mass will be

X=(0*M + 3M*13R)/(3M+M)

=>X=4R

so center of mass is at distance 4R and it reamins unchanged before and after collision happens.

During collision, centre of masses will be 5R apart. If collision takes place at dist x from origin,

after colllision x= (mx+3m(x+5R)}/6m =4R

=>4x+15R=24R=>x=9/4R