Question 36 of 210

A bullet of $4g$ mass is fired from a gun of mass $4kg.$ If the bullet moves with the muzzle speed of $50{ms}^{1},$ the impulse imparted to the gun and velocity of recoil of gun are

A$0.4kg{ms}^{-1},0.1{ms}^{-1}$B$0.2kg{ms}^{-1},0.05{ms}^{-1}$C$0.2kg{ms}^{-1},0.1{ms}^{-1}$D$0.4kg{ms}^{-1},0.05{ms}^{-1}$

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Answer: (B) $0.2kg{ms}^{-1},0.05{ms}^{-1}$

By momentum conservation,
$4\times {10}^{-3}(50-v)-4v=0$
$v=\dfrac{4\times {10}^{-3}\times 50}{4+4\times {10}^{-3}}\approx 0.05{ms}^{-1}$
Impulse $J=mv=4\times .05=0.2kgm{s}^{-1}$