A gun fires a bullet of mass $50 g$ with a velocity of $30 m s e c^{- 1}$ . Because of this the gun is pushed back with a velocity of $1 m s e c^{- 1}$ . The mass of the gun is

$15 k g$

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$30 k g$

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$1.5 k g$

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$20 k g$

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Solution

The correct option is C
$1.5 k g$

Explanation for the correct option:
Step 1: Given data:
Mass of bullet, $m_{b} = 50 g$
Velocity of bullet, $v_{b} = 30 m s e c^{- 1}$
Recoil velocity of gun, $v_{g} = 1 m s e c^{- 1}$
Step 2:Finding the mass of the gun:
Using principal of conservation of momentum
$\begin{array}{rcl} \Rightarrow & m_{g} v_{g} = m_{b} v_{b} \\ \Rightarrow & m_{g} = \frac{m_{b} v_{b}}{v_{g}} \\ \Rightarrow & m_{g} = \frac{50 x 10^{- 3} x 30}{1} \\ \Rightarrow & m_{g} = 1.5 k g \end{array}$
Hence, option C is correct.

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