Question

A closed tank filled with water is mounted on a cart. The cart moves with an acceleration ${}^{\prime }{a}^{\prime }$ on a plane road. What is the difference in pressure of points $B$ and $A$ shown in figure?

• A. $h\rho g$
• B. $(h+\ell )\rho g$
• C. $(hg+a\ell )\rho$
• D. $(h-\ell )\rho g$

Answer 1

The correct option is C $(hg+a\ell )\rho$

$Given:$ Acceleration of tank =$a$ $m/s^2$

$Solution:$ Now ,A/c to given figure pressure at point $A$ is given by

$\Rightarrow P_C-P_A=h\rho g$

$\Rightarrow P_A=P_C-h{\rho }_g........\left(i\right)$

Now, Pressure at point $C$

$\Rightarrow P_B-P_C=\ell \rho a$

$\Rightarrow P_C=P_B-\ell {\rho }_a......\left(ii\right)$

Now using Equation $\left(i\right)and\left(ii\right)$ we get$:-$

$\Rightarrow P_A=P_B-\ell {\rho }_a-h{\rho }_g$

$\Rightarrow P_B-P_A=\rho (hg+a\ell )$

$So,the$ $correct$ $option:C$