A) \[20N\]
B) \[12.5N\]
C) \[50N\]
D) \[75N\]
Correct Answer: C
Solution :
Mass and velocity of the bullet is \[{{M}_{b}}=25\,\,g=0.025\,\,kg,\,\,{{v}_{b}}=500\,\,m\,\,{{s}^{-1}}\] Mass of machine gun,\[{{M}_{g}}=12\,\,kg.\,\,{{V}_{g}}=?\] Magnitude of momentum of gun\[{{M}_{g}}{{v}_{b}}=-mv\] (Law of conservation of momentum)\[=0.025\times 500=12.5\,\,kg\,\,m\,\,{{s}^{-1}}\] As initial momentum of the gun is zero, the change in the momentum of the gun after it as fired one bullet in \[1/4\] second \[={{m}_{b}}{{v}_{b}}-0=12.5\,\,kg\,\,m\,\,{{s}^{-1}}\] \[\therefore \]Impulse\[=F\times t=12.5,\,\,F=\frac{12.5}{\left( {}^{1}/{}_{4} \right)}=50\,\,N\]
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