$A$ $U$-tube containing a liquid moves with a horizontal acceleration $a$ along a direction joining the two vertical limbs. The separation between these limbs is $d$. The difference in their liquid levels is

Define thrust and pressure and give their unit and dimensional formula.

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column,the temperature is constant,and surface tension is neglected,what is the depth of the lake (in $m$)?

In a $U$-tube as shown in the figure,water and oil are in the left and right sides of the tube,respectively. The heights from the bottom for the water and oil columns are $15 \; cm$ and $20 \; cm$,respectively. The density of the oil is ...... $kg/m^3$. [Take $\rho_{\text{water}} = 1000 \; kg/m^3$]

$A$ uniform long tube is bent into a circle of radius $R$ and it lies in a vertical plane. Two liquids of the same volume but densities $\rho$ and $\delta$ fill half the tube. The angle $\theta$ is

$A$ vertical $U$-tube of uniform cross-section contains water in both the arms. $A$ $10 \, cm$ glycerine column $(R.D. = 1.2)$ is added to one of the limbs. The level difference between the two free surfaces in the two limbs will be ...... $cm$.