question_answer

A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 kgm?3. The velocity with which gasoline begins to shoot out of the hole is

A)             \[27.8\,m{{s}^{-1}}\]         

B)             \[41.0\,m{{s}^{-1}}\]

C)             \[9.6\,m{{s}^{-1}}\]            

D)              \[19.7\,m{{s}^{-1}}\]

Correct Answer: B

Solution :

                   According to Bernoulli's theorem,                    \[{{P}_{B}}+h\rho g={{P}_{A}}+\frac{1}{2}\rho v_{A}^{2}\]                        \[(\text{As }{{v}_{A}}>>{{v}_{B}})\]                    \[3.10P+53\times 660\times 10=P+\frac{1}{2}\times 660v_{A}^{2}\]            Þ \[2.1\times 1.01\times {{10}^{5}}+3.498\times {{10}^{5}}\]\[=\frac{1}{2}\times 660\times v_{A}^{2}\]            Þ \[5.619\times {{10}^{5}}=\frac{1}{2}\times 660\times v_{A}^{2}\]             \ \[{{v}_{A}}=\sqrt{\frac{2\times 5.619\times {{10}^{5}}}{660}}\]= 41 m/s