Properties Of Solids And Liquids Question 230
Question: 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
Options:
A) The volume of the liquid flowing through the tube in unit time is $ A _{1}v _{1} $
B) $ v _{2}-v _{1}=\sqrt{2gh} $
C) $ v _{2}^{2}-v _{1}^{2}=2gh $
D)The energy per unit mass of the liquid is the same in both sections of the tube
Show Answer
Answer:
Correct Answer: C
Solution:
According to Bernoulli’s theorem,
$ P _{1}+\frac{1}{2}\rho v _{1}^{2}=P _{2}+\frac{1}{2}\rho v _{2}^{2} $
therefore $ P _{1}-P _{2}=\frac{1}{2}\rho \left( v _{2}^{2}-v _{1}^{2} \right) $
therefore $ h\rho g=\frac{1}{2}\rho \left( v _{2}^{2}-v _{1}^{2} \right) $ \ $ v _{2}^{2}-v _{1}^{2}=2gh $
Hence option (c) is correct.
