Assuming that the density of the metal is large compared to that of alcohol, it can be shown that. A metal ball immersed in alcohol weighs $W_1$ at  $0°\mathrm{C}$ and $W_2$ at $50°\mathrm{C}$. The coefficient of cubical expansion of the metal is less than that of the alcohol.

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