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A stick of length L and mass M lies on a...

A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed V collides elastically with the stick as shown in fig below .If after the collision , the ball comes to rest, then what should be the mass of the ball?

A

m=2M

B

m=M

C

`m= M//2`

D

`m = M//4`

Text Solution

Verified by Experts

The correct Answer is:
D
Applying the law of conservation of momentum
mv=MV
By conservation of angular momentum
`mv(L//2) = (ML^(2))/(12) omega`…………..(ii)
As the collision is elastic, we have
`1/2 mv^(2) = 1/2MV^(2) + 1/2I omega^(2)`……….(iii) or (`Lomega + V = evw` here e=1)
Substituting the valu,e we get: `m=M//4`
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