Question

A sniper fires a rifle bullet into a gasoline tank making a hole $53.0m$ below the surface of gasoline. The tank was sealed at $3.10atm$ . The stored gasoline has a density of $660k g \, m^{- 3}$ . The velocity with which gasoline begins to shoot out of the hole is

• A. $27.8m \, s^{- 1}$
• B. $41.0m \, s^{- 1}$
• C. $9.6m \, s^{- 1}$
• D. $19.7m \, s^{- 1}$

Answer 1

Answer: (B)

According to Bernoulli's theorem,
$P_{B}+h\rho g=P_{A}+\frac{1}{2}\rho v_{A}^{2}\left(A s v_{A} > > v_{B}\right)$
$3.10P+53\times 660\times 10=P+\frac{1}{2}\times 660v_{A}^{2}$
$\Rightarrow 2.1\times 1.01\times 10^{5}+3.498\times 10^{5}=\frac{1}{2}\times 660\times v_{A}^{2}$
$\Rightarrow 5.619\times 10^{5}=\frac{1}{2}\times 660\times v_{A}^{2}$
$\therefore v_{A}=\sqrt{\frac{2 \times 5.619 \times 10^{5}}{660}}=41ms^{- 1}$