$A$ liquid is kept in a closed vessel. If a glass plate (negligible mass) with a small hole is kept on top of the liquid surface,then the vapour pressure of the liquid in the vessel is

$A$ motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver $n$-times the water through the same pipe in the same time,the power of the motor must be increased as follows:

$A$ cylindrical tube,with its base as shown in the figure,is filled with water. It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta=45^{\circ}$. $P_1$ and $P_2$ are pressures at points $1$ and $2$,respectively,located at the base of the tube. Let $\beta=(P_1-P_2) / (\rho g d)$,where $\rho$ is the density of water,$d$ is the inner diameter of the tube,and $g$ is the acceleration due to gravity. Which of the following statement$(s)$ is(are) correct?
$(A)$ $\beta=0$ when $a=g / \sqrt{2}$
$(B)$ $\beta>0$ when $a=g / \sqrt{2}$
$(C)$ $\beta=\frac{\sqrt{2}-1}{\sqrt{2}}$ when $a=g / 2$
$(D)$ $\beta=\frac{1}{\sqrt{2}}$ when $a=g / 2$

An air bubble rises from the bottom of a lake to the surface. If its radius increases by $200 \%$ and the atmospheric pressure is equal to a water column of height $H$,then the depth of the lake is ..... $H$.

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density $d.$ The area of the base of both vessels is $S$ but the height of liquid in one vessel is $x_{1}$ and in the other,$x_{2}$. When both cylinders are connected through a pipe of negligible volume very close to the bottom,the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is

$A$ fluid container containing a liquid of density $\rho$ is accelerating upward with acceleration $a$ along an inclined plane of inclination $\alpha$ as shown. Then the angle of inclination $\theta$ of the free surface is: