What is the ratio$\frac{k_1}{k_2}$ Can be expressed. When a block of iron floats in mercury at $0°\mathrm{C}$, fraction $k_1$ Of its volume is submerged, while at the temperature $60°\mathrm{C}$, a fraction $k_2$ is seen to be submerged. If the coefficient of volume expansion of iron is ${\gamma }_{Fe}$ And that of mercury is ${\gamma }_{Hg}$,

A hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$, Fig. $14.79$. The volume of the remaining cylinder is $V$ and its mass $\mathrm{M}$. It is suspended by a string in a liquid of density $\rho$ where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is

A wooden block, with a coin placed on the top, floats in water as shown in figure (Fig. $14.80$). The distance $l$ and $h$ Are shown here. sometimes the coin falls into the water. Then

The spring balance $A$ reads $2 \mathrm{kg}$ with a block $\mathrm{m}$ suspended from it. A 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 the figure (Fig. $14.81$). In this situation :

Two solid spheres $A$ and $B$ of equal volumes but of different densities $A$ and $B$ are connected by a string. They are fully immersed in a fluid of density $d_F$.  They get arranged into an equilibrium state as shown in the figure, Fig. $14.82$ with a tension in the string. The arrangement is possible only if

A jar is filled with two non-mixing liquids $1$ and $2$ having densities ${\rho }_1$ and ${\rho }_2$ respectively. A solid ball, made of a material of density ${\rho }_3$ is dropped in the jar. It comes to equilibrium in the position shown in the figure (Fig. $14.83$). Which of the following is true for ${\rho }_3, {\rho }_1$ and ${\rho }_2$ ?

A liquid $X$ of density $3.36 \mathrm{g}{ \mathrm{cm}}^{-3}$ and height $10 \mathrm{cm}$ is poured in a $\mathrm{U}$-tube, which contains $Hg$ Fig. $14.84$. Another liquid $Y$ is poured in left arm with height $8 \mathrm{cm}$, upper levels of $X$ and $Y$ are the same. What is density of $Y$ ?