A rifle man, who together with his rifle has a mass of 100kg, stands on a smooth surface and fires 10 shots horizontally. Each bullet has a mass 10g and a muzzle velocity of 800m/s. What velocity does the rifle man acquire at the end of 10 shots?
A
0.8m/s
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B
0.5m/s
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C
0.3m/s
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D
1.2m/s
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Solution
The correct option is A0.8m/s Let m1 and m2 be the masses of the bullet and the rifleman and v1 and v2 be their respective velocities after the first shot.
Initially, the rifleman and bullet are at rest, therefore initial momentum of system =0.
As external force is zero, momentum of system remains conserved i.e.
Initial momentum = Final momentum
After first shot, m1v1+m2v2=0
or v2=−m1v1m2
(∵m1<<m2,m2≈100kg) =−(10×10−3kg)(800m/s)100kg=−0.08m/s
After 10 shots, 10m1v1+m2v′2=0
Therefore, velocity acquired after 10 shots v′2=−10m1v1m2=10v2=10×(−0.08)=−0.8m/s
(-ve sign indicates velocity of man is opposite to bullet's velocity)