Q. 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) $27.8ms^{- 1}$
B) $41.0ms^{- 1}$
C) $9.6ms^{- 1}$
D) $19.7ms^{- 1}$
Explanation
(b) According to Bernoulli’s theorem
$P_{B} + h\rho g = P_{A} + \frac{1}{2}\rho v_{A}^{2}\ \ \ \lbrack As\ v_{A} > \ > v_{B}\rbrack$
$3.10P + 53 \times 660 \times 10 = P + \frac{1}{2} \times 660v_{A}^{2}$
$\Rightarrow 2.1 \times 1.01 \times 10^{5} + 3.498 \times 10^{5} = \frac{1}{2} \times 660 \times v_{A}^{2}$
$\Rightarrow 5.619 \times 10^{5} = \frac{1}{2} \times 660 \times v_{A}^{2}$
$\therefore v_{A} = \sqrt{\frac{2 \times 5.619 \times 10^{5}}{660}} = 41\ m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.