What is the recoil velocity of the gun of mass $8$ kg when a bullet of mass $10$ g is fired from it with a velocity of $400$ m/s ?

5

m/s

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2

m/s

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50

m/s

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0.5

m/s

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Solution

The correct option is D $0.5$ m/s
Given :
mass of the gun $m_{g} = 8$ kg
mass of the bullet $m_{b} = 0.01$ kg
velocity of the bullet $v_{b} = 400$ m/s
recoil velocity of the gun $V_{g} = ?$
As no external force is acting on the system, the total linear momentum of the system is conserved.
Conservation of linear momentum : $P_{i} = P_{f}$
Initial momentum $P_{i} = 0$ as the gun and the bullet do not move.
Final momentum $P_{f} = m_{g} V_{g} + m_{b} v_{b}$
$∴$ $0 = m_{g} V_{g} + m_{b} v_{b}$
$\Rightarrow 0 = 8 V_{g} + (0.01) (400)$
$\Rightarrow | V_{g} | = 0.5$ m/s

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