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4-1.Newton's Laws of Motion
medium
A bullet of $'4\,g'$ mass is fired from a gun of mass $4 \,{kg}$. 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
$0.4\, {kg} \,{ms}^{-1}, 0.1\, {ms}^{-1}$
B
$0.2 \,{kg} \,{ms}^{-1}, 0.1\, {ms}^{-1}$
C
$0.2 \,{kg} \,{ms}^{-1}, 0.05\, {ms}^{-1}$
D
$0.4 \,{kg}\, {ms}^{-1}, 0.05 \,{ms}^{-1}$
(JEE MAIN-2021)
Solution
By momentum conservation
$4 \times 10^{-3}(50-v)-4 v=0$
$v=\frac{4 \times 10^{-3} \times 50}{4+4 \times 10^{-3}} \approx 0.05\, m s^{-1}$
Impulse $=J=m v=4 \times 0.05=0.2 \,{kgms}^{-1}$
Standard 11
Physics
