There is a small hole in the bottom of a fixed container containing a liquid up to height $h.$The top of the liquid, as well as the hole at the bottom, are exposed to atmosphere. As the liquid comes out of the hole. (Area of the hole is $a$ and that of the top surface is $A$) 

The velocity of the liquid coming out of a small hole of a large vessel containing two different liquids of densities $2\rho$ and $\rho$as shown in the figure is

A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then radius $R$ is equal to :

A cup of water is placed in a car moving at a constant acceleration $a$ to the left. Inside the water is a small air bubble. The figure correctly shows the shape of the water surface and the direction of motion of the air bubble is-

A 

B 

C 

D 

A stick of square cross-section $(5 \mathrm{cm} \times 5 \mathrm{cm})$ and length $‘4 \mathrm{m}’$ weighs $2.5 \mathrm{kg}$ is in equilibrium as shown in the figure below. Determine its angle of inclination (in degree) in equilibrium when the water surface is $1 \mathrm{m}$ above the hinge. 

A non-viscous liquid of constant density $1000 \mathrm{kg} {\mathrm{m}}^{-3}$ flows in a streamlined motion along a tube of the variable cross-section. The tube is kept inclined in the vertical plane as shown in the figure. The area of cross-section of the tube at two points $P$ and $Q$ at heights of $2 \mathrm{m}$ and $5 \mathrm{m}$ are respectively $4 \times {10}^{–3} {\mathrm{m}}^2 \& 8 \times {10}^{–3} {\mathrm{m}}^2.$ The velocity of the liquid at point $P$ is $1 \mathrm{m} {\mathrm{s}}^{-1}$. If the work done per unit volume by the pressure is $\left(1161\right)\mathrm{\alpha } \mathrm{joule} {\mathrm{m}}^{-3}$as the liquid flows from point $P$ to $\mathrm{Q}$.then $\mathrm{\alpha }$ will be $(g=9.8 \mathrm{m} {\mathrm{s}}^{-2})$