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A particle mass m is revolving around a ...

A particle mass m is revolving around a planet in a circular orbit of radius R. A the instant the particle have velocity `overset( 1) ( V)`, another particle of mass `( m )/( 4)` collides perfectly inelastically with the first particle. If the combine body - wasfound to follow elliptical path with velocity `( 5 overset( 1)( V))/( 8)` then the velocity of second particle just before collision is `:` `( | overset( 1)( V) | = V)`

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

Text Solution

Verified by Experts

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)`
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