Embibe Experts Solutions for Chapter: Fluid Mechanics, Exercise 6: Exercise (Analytical Questions)

To what height $h$ should a cylindrical vessel of diameter $d$ be filled with a liquid so that the liquid force on the vertical surface of the vessel be equal to the force on the bottom?

A solid uniform ball having volume $V$ and density $\rho$ floats at the interface of two immiscible liquids as shown in figure. The densities of the upper and the lower liquids are ${\rho }_1$ and ${\rho }_2$, respectively, such that ${\rho }_1<\rho <{\rho }_2$. What fraction of the volume of the ball will be in the lower liquid?

A homogeneous solid cylinder of length $L \left(L<\frac{H}{2}\right)$, cross-sectional area $\frac{A}{5}$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $\frac{L}{4}$ in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure $P_{\mathrm{o}}$. Then, density $D$ of solid is given by :-

A ball rises to surface at a constant velocity in liquid whose density is $4$ times than that of the material of the ball. The ratio of the force of friction acting on the rising ball and its weight is,

A wooden cube first floats inside water when a $200 g$ mass is placed on it. When the mass is removed, the cube rises by $2 \mathrm{cm}$. The side of the cube is
 

A U-tube contains two liquids in static equilibrium: water of density, ${\rho }_{\mathrm{w}}$$=1000 \mathrm{kg} {\mathrm{m}}^{-3}$ is in the right arm, oil of unknown density $\rho$ is in the left arm as shown in figure. Measurements give, $l=135 \mathrm{mm}$ and $d=12.5 \mathrm{mm}$. The density of oil is,

There is a hole in the bottom of the tank having water. If total pressure at the bottom is $3 \mathrm{atm}$ $\left(1 \mathrm{atm}={10}^5 \mathrm{N} {\mathrm{m}}^{-1}\right)$ then the velocity of water flowing from the hole is

Water is moving with a speed of $5.0 \mathrm{m} {\mathrm{s}}^{-1}$ through a pipe will cross-sectional area of $4.0 {\mathrm{cm}}^2$. The water gradually descends $10 \mathrm{m}$ as the pipe increase in area to $8.0 {\mathrm{cm}}^2$. If the pressure at the upper level is $1.5\times {10}^5 \mathrm{Pa}$, the pressure at lower level will be,