A particle of mass m is revolving around a planet in a circular orbit of radius R. At the instant the particle has velocity `vec V` another particle of mass `m/2` moving at velocity ` (vec V)/2` collides perfectly in-elastically with the first particle. The new path of the combined body will take is

Options

A. `(7V)/8` in direction of first particle
B. `(7V)/8` in opposite direction of first particle
C. `(5V)/8`in direction of first particle
D. `(5V)/8` in direction opposite to first particle

Answer

B

Explanation

Let the velocity of first particle be x
on conserving momentum
`rArrmV+(m)/(4)x=(m+m/4)((5V)/(8))rArrmV+(mx)/(4)=(5m)/(4)xx(5V)/(8)`
`rArr (mx)/(4)=(25mV)/(32)-mV rArr (mx)/(4)=(-7mV)/(32)rArr x=(-7V)/(8)`