A machine gun fires a bullet of mass 40g with a velocity 1200m/s. The man holding it can exert a maximum force of 144N on the gun. How many bullets can be fired per second at the most?
A
Only one
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B
Three
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C
Can fire any number of bullets
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D
144×48
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Solution
The correct option is B Three
Step 1: Newton's Second Law,
From Newton's second law
F=dPdt....(1)
Where, P=mv is the momentum
Step 2: Total bullets fired per sec
Let n be the total number of bullets fired
The force exerted by man must balance the change in momentum of the bullets per second.
∴P=nmv;m and v are constant (Given)
⇒F=ddt(nmv)
⇒dndt=Fmv=144(N)40×10−3(kg)×1200(m/s)=3
Hence total number of bullets fired per second i.e., dndt=3.