Q.

A plate of mass M remains in equilibrium in air when n bullets are fired per second on it. The mass of each bullet is m and it strikes the plate with speed v' If the coefficient of restitution is e, then (M>>m)

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a

M=nm(1+e)Vg

b

M=nmvg

c

M=2nme+e2g

d

M=2nmg

answer is A.

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Detailed Solution

see fig. (4) the change in momentum of Bullet = m v e - (-m v) = m v (1+e)given that n bullets strike per second '. Force exerted by the bullets  =n[mv(1+e)] upwards   Now n[mv(1+e)]=Mg (∵F=Mg downwards ) so, M=nmv(1+e)g
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