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

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20 kg

30 kg

90 kg

50 kg

answer is C.

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Detailed Solution

A gun fires a shell of mass

1.5 kg

with a velocity of

150 m / s

recoils with a velocity of

1.5 m / s

. The mass of the gun is

90 kg .

Given data in the problem,
Shell mass,

m = 1.5 kg

Velocity of shell,

v_{1} = 150 m / s

Velocity of recoil,

v_{2} = 2.5 m / s

Gun mass

= M

And according to the conservation of momentum,

m v_{1} = m v_{2}

\Rightarrow 1.5 \times 150 = M \times 2.5

\Rightarrow M = \frac{1.5 \times 150}{2.5}

\Rightarrow M = 90 kg

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