Q.

A plate 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. The coefficient of restitution is e=0.5. The mass of the plate is

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a

M=2mnv3g

b

M=mnvg

c

M=2mnvg

d

M=3mnv2g

answer is A.

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Detailed Solution

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The change in momentum of one bullet=final momentum-initial momentum

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=mv2--mv=32mv Also, given that n bullet strikes per second. Force exerted by the bullets=32mnv Since, the plate remains in equilibrium Force exerted by the bullets=weight of the plate 32mnv=Mg or M=3mnv2g (where M=mass of the plate)

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A plate 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. The coefficient of restitution is e=0.5. The mass of the plate is