B M Sharma Solutions for Chapter: Fluid Mechanics, Exercise 2: DPP 4.2

A uniform rod of density$\rho$ is placed in a wide tank containing a liquid of density ${\rho }_0({\rho }_0>\rho ).$ The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position, the rod makes an angle$\theta$ with the horizontal. Then,

The spring balance $A$ reads $2 \mathrm{kg}$ with a block suspended from it. Another balance $B$ reads $5 \mathrm{kg}$ when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in figure. In this situation

A body totally immersed in water is raised in the water by a height $h.$ The density of the body is $d$ and the density of water is $d_0$, while the volume of the body is$V$and $d>d_0.$ Which of the given statements will be true?

A vessel with water is placed on a weighing pan and it reads $600 \mathrm{g}$. Now a ball of $40 \mathrm{g}$ and density$0.80 \mathrm{g} {\mathrm{cc}}^{-1}$ is sunk into the water with a pin of negligible volume as shown in the figure, keeping it sunk. What will be the reading of weighing pan? 

A hollow sphere of relative density $2$ floats completely immersed on the surface of water. If the volume of the sphere is $V$, then find the volume of the cavity.

A cube of each side $L$ floats in a liquid of density$3$ times the density of cube. What length of the cube will be outside the liquid? 

A wooden ball of density$\text{ρ}$ is immersed in a liquid of density $\text{σ}$ to a depth $H$ and then released. Find the height $h$ above the surface to which the ball rises.

Two solids $A$ and $B$ float in water. It is observed that $A$ floats with $\frac{1}{2}$ of its body immersed in water and B floats with $\frac{1}{4}$ of its volume above the water level. Find the ratio of the density of $A$ to that of $B$.