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?

Options

A. m=2M
B. m=M
C. m=M/2
D. m=M/4

Answer

4

Explanation

Applying the law of conservation of momentum mv=Mv…(i)By conservation of angular momentum`mv(L/2)=((ML^2)/12)omega`..(ii) As the collision Is elastic, we have `1/2mv^2=1/2MV^2+1/2omega^2`..(iii) or (`Lomega+V=ev` where e=1)Subtituting the Values, we get m=M/4.