Question

Two pieces, one of mass M and the other of mass 4M. After the explosion, the mass M ends up traveling in the same circular orbit, but in opposite direction. After the explosion the mass 4M is :

• A. In a circle orbit
• B. unbound
• C. elliptical orbit
• D. data is insufficient to determent the nature of the orbit

Answer 1

The correct option is B unbound

According to conservation of linear momentum:

$5M\times v_0=-M{v}_0+4MV$

$6M\times v_0=4MV$

$V=\frac{3}{2}{v}_0$

$V>v_0$,

so cannot be in circular orbit.

We have two options: a) unbound and b) elliptical orbit

Energy of $4M$ mass:$\frac{-4MGMe}{r}+\frac{1}{2}\times 4M\times V^2$

$=\frac{-4MGMe}{r}+\frac{1}{2}\times 4M\times \frac{9}{4}{v}_0^2(asV=\frac{3}{2}{v}_0)$

$\frac{4M{v}_0^2}{r}=\frac{4MGMe}{r^2}$

$v_0^2=\frac{GMe}{r}$

Now putting $v_0^2$ and solving energy > 0

Clearly we get unbound.

Answer: 2.