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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 the figure. If after the collision the ball comes to rest, then what would be the mass of the ball?

A

(a)m = 2M

B

(b)m = M

C

(c)m = M/2

D

(d)m = M/4

Text Solution

Verified by Experts

The correct Answer is:
D
According to law of conservation of linear momentum
`mv=MV" …(i)"`
According to law of conservation of angular momentum,
`mv.(L)/(2)=(ML^(2))/(12)omega" ….(ii)`
Since, the collision is elastic, therefore `(1)/(2)mv^(2)=(1)/(2)MV^(2)+(1)/(2)lomega^(2)`
Putting the values of `omega` and V in above equation,
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