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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?

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5m/s

2m/s

50 m/s

0.5 m/s

answer is D.

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Detailed Solution

Concept: The system's initial momentum (rifle and bullet)

= (m_{1} + m_{2}) v = 0

Given the situation,
The rifle's mass is

m_{1} = 8 kg

The bullet's mass is

m_{2} = 10 g = 0.01 kg

.
The rifle's recoil velocity is equal to v1.
The bullet is discharged at a velocity of

v_{2} = 400 m / s .

The rifle is initially at rest.
As a result, its initial velocity is v= 0.
The system's initial momentum (rifle and bullet)

= (m_{1} + m_{2}) v = 0

After firing, the total momentum of the system (rifle and bullet) is:

8 vg + (0.01) = m_{1} v_{1} + m_{2} v_{2} (400)

Apply the Law of Conservation of Linear Momentum now:
After shooting, initial momentum (rifle and bullet) = total momentum (rifle and bullet):
That is, Pi = Pf.
8vg + (0.01) = 0 (400)

vg = - 0.5 m / s vg = - 0.5 m / s vg = - 0.5 m / s

The gun recoils backwards with a velocity of 0.5 m/s, as shown by the negative sign.
0.5 m/s |vg|
As a result, the recoil velocity of the gun is 0.5 m/s.
Hence, the correct option is 4.

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