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Question

From a rifle of mass 4 kg, a bullet of mass 50 g is fired with a velocity of 35 ms1​ with respect to the ground. Calculate the recoil velocity of the rifle.


A

1 ms1

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B

0.4375 ms1

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C

0 ms1

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D

2.5 ms1

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Solution

The correct option is B

0.4375 ms1


Let initial velocity of bullet be u1 and initial velocity of rifle be u2.
u1 =u2 =0 (Initially bullet and rifle system was at rest)
Let, mass of rifle ,m1 = 4kg

Mass of bullet, m2 = 501000=0.05kg

Final velocity of bullet, v2 = 35 ms1
Final velocity of rifle, v1 = v

From principle of conservation of linear momentum:
Initial momentum is equal to final momentum
.
m1u1+m2u2=m1v1+m2v2
4×0+0.05×0=4×v+0.05×35
0=1.75+4v
v=0.4375 ms1

The negative sign indicates that the rifle recoils in the opposite direction with the velocity of 0.4375 ms1.


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