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A smooth ball 'A' moving with velocity '...

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

A

`(1)/(3) mV^(2)`

B

`(2)/(3) mV^(2)`

C

0

D

`(1)/(6)mV^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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)`
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