In the figure,chamber $A$ contains a gas,a movable chamber $B$ is placed on top of the gas and it contains $n$ metal balls. The weight of chamber $B$ and the balls is supported by the gas. Chamber $C$ is a vacuum. Let the gas be in equilibrium at pressure $P$. Let $P^{\prime}$ be the pressure if one of the balls is taken away. Find $(P-P^{\prime}) / P$.

The figure shows a container filled with a liquid of density $\rho$. Four points $A, B, C$ and $D$ lie on the diametrically opposite points of a circle as shown. Points $A$ and $C$ lie on a vertical line,and points $B$ and $D$ lie on a horizontal line. Which of the following statements is incorrect? (Here,$p_A, p_B, p_C, p_D$ are the absolute pressures at the respective points.)

$A$ vertical triangular plate $ABC$ is placed inside water with side $BC$ parallel to the water surface as shown. The force on one surface of the plate by water is (density of water is $\rho$ and atmospheric pressure is $P_0$).

In the previous problem,if $15.0 \; cm$ of water and spirit each are further poured into the respective arms of the tube,what is the difference in the levels of mercury in the two arms (in $; cm$)? (Specific gravity of mercury $= 13.6$)

In which layer of the atmosphere is water vapour present?

Consider a mercury-filled tube as shown in the figure below. Which of the following options about the pressures at the lettered locations $(A, B, C, D)$ is true?