Question

A liquid stands at the plane level in the U-tube when at rest. If areas of cross-section of both the limbs are equal, what will be the difference in heights $h$ of the liquid in the two limbs of U-tube, when the system is given an acceleration a in horizontal direction towards right as shown?

• A. $\frac{g}{a}\frac{L^2}{H}$
• B. $\frac{La}{g}$
• C. $\frac{L^2}{H}\frac{a}{g}$
• D. $\frac{Lg}{a}$

Answer 1

Answer: (B)

$\frac{La}{g}$

Due to acceleration in the horizontal direction of magnitude $a$, the pressure difference between the two extreme points of the horizontal tube=$\rho aL$.

Since this would be compensated by the difference in height of liquid in the two tubes, $\rho g(h_1-h_2)=\rho aL$

$⟹h_1-h_2=\frac{La}{g}$