Question

If a vessel containing a fluid of density $p$ upto height $h$ is accelerated vertically downwards with acceleration $a_{0}$. Then the pressure by fluid at the bottom of vessel is given by the equation ________$\left(P_{0}\right.$ denotes the atmospheric pressure and ' $g$ ' denotes the acceleration due to gravity)

• A. $P=P_{0}+\rho g h+\rho h a_{0}$
• B. $P=P_{0}+\rho g h$
• C. $P=P_{0}+\rho h\left(g-a_{0}\right)$
• D. $P=P_{0}-\rho g h$

Answer 1

Answer: (C)

When a vessel containing a fluid of density $\rho$ upto height $h$ is accelerated downwards with acceleration $a_{0}$, then net gravitational acceleration acting on the fluid
$g'=g-a_{0} \ldots .$ (i)
Hence, the pressure by the fluid at the bottom of vessel is given as
$p=p_{0}+\rho g h=p_{0}+\rho\left(g-a_{0}\right) h[$ From Eq. (i) $]$