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A rifle of 20 kg mass can fire 4 bullets per second. The mass of each bullet is $35 \times 10^{- 3} k g$ and its final velocity is $400 m s^{- 1}$ . Then what force must be applied on the rifle so that it does not move backward while firing the bullets?

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-112 N

-56 N

80 N

28 N

answer is D.

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Detailed Solution

From conservation of momentum

$M V + (4 m v) = 0$

$\Rightarrow$ $V = - \frac{4 m v}{M} = - \frac{4 \times 35 \times 10^{- 3} \times 400}{20}$

$= - 2.8 m s^{- 1}$

Force applied on the rifle,

$F = \frac{M V}{t} = - \frac{20 \times 2.8}{1}$

$= - 56 N$

alternatively:

F= N m v/t

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