A smooth ball `'A'` moving with velocity `'V'` collides with another smooth identical ball at rest. After collision both the balls move with same speed with angle between their velocities `60^(@)`. No external force acts on the system of balls.

If the kinetic energy lost is fully converted to heat then heat produced is

Options

A. `(1)/(3) mV^(2)`
B. `(2)/(3) mV^(2)`
C. 0
D. `(1)/(6)mV^(2)`

Answer

D

Explanation

From conservation of momentum
`mv=mv' cos 30^(@)+mv' cos 30^(@)`
`:. V' =(v)/(2 cos 30^(@))=(v)/(sqrt(3))`
Loss in kinetic energy
`=(1)/(2)mv^(2)-2xx(1)/(2)m((v)/(sqrt(3)))^(2)=(1)/(6)mv^(2)`