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Q.

A stick of length I 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. If after
the collision the ball comes to rest, then what should be the mass of the ball ?

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a

m=2M

b

m=M

c

m=M/2

d

m=M/4

answer is D.

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Detailed Solution

Applying the law of conservation of momentum
mv=MV…………………(1)
By conservation of angular momentum
$mv (L / 2) = (\frac{{ML}^{2}}{12}) ω$ ………………..(2)
As the collision is elastic, we have
$\frac{1}{2} {mv}^{2} = \frac{1}{2} {MV}^{2} + \frac{1}{2} {Iω}^{2}$ …………..(3)
Substituting the values, we get
m = M / 4

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A stick of length I 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. If afterthe collision the ball comes to rest, then what should be the mass of the ball ?