A) 1.6 \[cm{{s}^{-1}}\]
B) 0.5 \[cm{{s}^{-1}}\]
C) 2 \[cm{{s}^{-1}}\]
D) 3 \[cm{{s}^{-1}}\]
Correct Answer: A
Solution :
Here, mass of gun, M = 100 kg Mass of shell, m = 0.02 kg Speed of shell, \[v=80\,\,m{{s}^{-1}}\] and let recoil speed of gun = - V As initially both the gun and the shell are at rest before firing, so the initial momentum \[({{P}_{i}})\] of the system = 0 Final momentum (Pf) of the system after firing \[=MV+mv=100\,\,V+0.02\times 80\] According to law of conservation of linear momentum, \[{{P}_{i}}={{P}_{F}}\] \[0=100\,V+1.6\] \[\Rightarrow \] \[V=\frac{-1.6}{100}=0.016\,\,m{{s}^{-1}}\] \[\therefore \]Recoil speed of gun,\[V=0.016\,\,m{{s}^{-1}}=1.6\,\,c{{s}^{-1}}\]
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