A ball of mass 1 kg moving along x-direction collides elastically with a stationary ball of mass m. The first ball (mass = 1 kg) recoils at right angle to its original direction of motion. If the second ball starts moving at an angle `30^(@)` with the X-axis, then the value of m must be

Options

A. 0.5 kg
B. 1.5 kg
C. 2.5 kg
D. 2 kg

Answer

D

Explanation

The given data can be digrammatically represented a below,

According to the conservation of linear momentum,
`(1)(mu) = mv_2 cos (30^@) …(1) ( therefore "Along x - direction ")`
`(1) (v_1) = mv_2 sin (30^@) ….(2) (therefore "Along y - direction )`
`=mv_2 = 2v_1`
On solving (1) and (2) ,
`u = sqrt3 v_1`
Given, the collision is elastic
`therefore (1)/(2) mu^2 = (1)/(2) v_1^2 + (1)/(2) mv_2^2`
`rArr (1)/(2) u^2 -(1)/(2) ((mu^2)/(3)) + (1)/(2m) ((2)/(sqrt3) mu^2)`
`rArr (1)/(2) = (1)/(6) + (2) /(3m)`
`therefore m = 2kg`.