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

Explanation

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