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Q.

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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a

5m/s

b

2m/s

c

50 m/s

d

0.5 m/s  

answer is D.

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Detailed Solution


Concept: The system's initial momentum (rifle and bullet) = (m1+m2) v= 0
Given the situation,
The rifle's mass is m1=8 kg
The bullet's mass is m2= 10g= 0.01 kg.
The rifle's recoil velocity is equal to v1.
The bullet is discharged at a velocity of v2= 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) = (m1+m2) v= 0
After firing, the total momentum of the system (rifle and bullet) is:
8vg + (0.01) = m1v1 +m2 v2(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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