TOPICWISE QUESTIONS

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 the holes are same. Then, the radius $R$ is equal to,

At what speed is the velocity head of water equal to the pressure head of $40 \mathrm{cm}$ of $\mathrm{Hg}$?

A fixed cylindrical tank having large cross-sectional area is filled with two liquids of densities $\mathrm{\rho }$ and $2\mathrm{\rho }$ and in equal volumes as shown in the figure. A small hole of area of cross-section $a$ is made at height $\frac{h}{2}$ from the bottom. Calculate the velocity of efflux.

A large tank is filled with two liquids of specific gravities $2\mathrm{\sigma }$and $\mathrm{\sigma }$. Two holes, $A$ and $B$, are made on the wall of the tank as shown in the figure. Find the ratio of the distance from $O$ of the points on the ground where the jets from holes $A$ and $B$ strike.

A $U$-tube of base length $l$ filled with same volume of two liquids of densities $\mathrm{\rho }$ and $2\mathrm{\rho }$ is moving with an acceleration $a$ on a 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,

If the terminal speed of a sphere of gold ($\text{density}=19.5 \mathrm{kg} {\mathrm{m}}^{-3}$) is $0.2 \mathrm{m} {\mathrm{s}}^{-1}$ in a viscous liquid, then find the terminal speed of sphere of silver ($\text{density}=10.5 \mathrm{kg} {\mathrm{m}}^{-3}$) of the same size in the same liquid ($\text{density}=10.5 \mathrm{kg} {\mathrm{m}}^{-3}$).

A spherical solid ball of volume $V$ is made of a material of density ${\rho }_1$. It is falling through a liquid of density ${\rho }_2$ $\left({\mathrm{\rho }}_2<{\mathrm{\rho }}_1\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e.,$F_{\mathrm{viscous}}=-k{v}^2 (k>0)$, then the terminal speed of the ball is,

If a ball of steel $({\mathrm{\rho }}_{\mathrm{ball}}=7.8 \mathrm{g} {\mathrm{cm}}^{-3})$ attains a terminal velocity of $10 \mathrm{cm} {\mathrm{s}}^{-1}$ when falling in water $\left({\mathrm{\eta }}_{\mathrm{water}}=8.5 \times {10}^{-4} \mathrm{Pa} \mathrm{s}\right)$, then its terminal velocity in glycerine $\left({\mathrm{\sigma }}_{\mathrm{glycerine}}=1.2 \mathrm{g} {\mathrm{cm}}^{-3}, {\mathrm{\eta }}_{\mathrm{glycerine}}=13.2 \mathrm{Pa} \mathrm{s}\right)$ would nearly be,