Question

A U-tube of base length "I" filled with same volume of two liquids of densities p and 2p is moving with an acceleration "a" on, the horizontal, plane as shown in the figure. If.the height difference between the two surfaces (open to atmosphere) becomes zero then the height h is given by:

• A. $\frac{a}{2g}l$
• B. $\frac{3a}{2g}l$
• C. $\frac{a}{g}l$
• D. $\frac{2a}{3g}l$

Answer 1

The correct option is B $\frac{3a}{2g}l$

at equilibrium pressure at both point in the bottom end will be same
pressure at the bottom of lighter liquid(left) $=$pressure at the bottom of denser liquid(right)
$\rho gh+\rho a\frac{l}{2}+2\rho a\frac{l}{2}=2\rho gh\frac{3}{2}pal=\rho ghh=\frac{3a}{2g}l$