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

According to the law of conservation of momentum,
`1xxu_(1)=mv_(2)cos30^(@)" "("X-axis")`
`implies" "u_(1)=(sqrt(3))/(2)mv_(2)`
and `1xx v_(1)=mv_(2)sin30^(@)" "("Y-axis")`
`v_(1)=(1)/(2)mv_(2)`
From kinetic energy conservation,
`(1)/(2)u_(1)^(2)=(1)/(2)v_(1)^(2)+(1)/(2)mv_(2)^(2)`
`implies" "u_(1)^(2)-v_(1)^(2)=(1)/(2)mv_(2)^(2)`
On putting the values of `u_(1)` and `v_(1)`, we get
`(3)/(4)m^(2)v_(2)^(2)-(1)/(4)m^(2)v_(2)^(2)=(1)/(2)mv_(2)^(2)`
`implies" "m=2kg`