A) \[\text{1}.\text{6 cm}{{\text{s}}^{\text{-1}}}\]
B) \[0.\text{5 cm}{{\text{s}}^{\text{-1}}}\]
C) \[\text{2 cm}{{\text{s}}^{\text{-1}}}\]
D) \[\text{3cm}{{\text{s}}^{-1}}\]
Correct Answer: A
Solution :
Here, mass of gun, \[\text{M }=\text{1}00\text{ kg}\] Mass of shell, m = 0.02 kg Speed of shell, \[\text{v }=\text{ 8}0\text{ m}{{\text{s}}^{-1}}\]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 \[({{P}_{f}})\] of the system after firing \[=MV+mv=100V+0.02\times 80\] According to law of conservation of linear momentum, \[{{P}_{i}}={{P}_{F}}\] \[0=100V+1.6\] \[\Rightarrow \] \[V=\frac{-1.6}{100}=0.016\text{m}{{\text{s}}^{\text{-1}}}\] \[\therefore \] Recoil speed of gun, \[V=0.016m{{s}^{-1}}=1.6c{{s}^{-1}}\]
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