A gun fires a shell of mass $1.5$ kg with velocity of $150$ m/s and recoils with a velocity of $2.5$ m/s.
Calculate the mass of the gun.

20

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30

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90

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60

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Solution

The correct option is C $90$ kg
Mass of shell $= 1.5$ kg
Velocity of shell $V_{1} = 159 m / s$
Recoil velocity $= 2.5$ m/s
mass of gun $= M$
According to the conservation of momentum,
$m v_{1} = m v_{2}$
$\begin{matrix} 1.5 \times 150 = M \times 2.5 M = \frac{1.5 \times 159}{2.5} M = 90 k g \end{matrix}$

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