From a stationary tank of mass $125000$ pound, a small shell of mass $25$ pound is fired with a muzzle velocity of $1000 f t / s e c$ . The tank recoils with a velocity of ..........

0.1 f t / s e c

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0.2 f t / s e c

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0.4 f t / s e c

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0.8 f t / s e c

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Solution

The correct option is B $0.2 f t / s e c$
Given:
Mass of the tank $M = 125000 p o u n d$
Mass of the shell $m = 25 p o u n d$
Velocity of the shell $v = 100 f t / s e c$
Recoil velocity of the tank $V = ?$
Since There is no external force acting, we can apply conservation of momentum.
According to the conservation of momentum,
$Initial momentum of (tank+shell) = Final momentum of (tank + shell)$
$(M + m) \times 0 = M \times V + m \times v$
$\Rightarrow 0 = 125000 \times V + 25 \times 1000$
$\Rightarrow V = - \frac{25000}{125000} = - \frac{1}{5} = - 0.2 f t / s e c$
The -ve sign indicates that the tank will recoin in the opposite direction to the direction of motion of the shell.

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From a stationary tank of mass 125000 pound, a small shell of mass 25 pound is fired with a muzzle velocity of 1000 ft/sec. The tank recoils with a velocity of ..........

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