$A$ rectangular block is $5 \ cm \times 5 \ cm \times 10 \ cm$ in size. The block is floating in water with the $5 \ cm$ side vertical. If it floats with the $10 \ cm$ side vertical,what change will occur in the level of water?

$A$ cone of radius $R$ and height $H$ is hanging inside a liquid of density $\rho$ by means of a string,as shown in the figure. The force due to the liquid acting on the slant surface of the cone is:

An object with uniform density $\rho$ is attached to a spring that is known to stretch linearly with applied force. When the spring-object system is immersed in a liquid of density $\rho_1$,the spring stretches by an amount $x_1$ (where $\rho > \rho_1$). When the experiment is repeated in a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$),the spring stretches by an amount $x_2$. Neglecting any buoyant force on the spring,the density of the object is:

What is buoyant force?

Spheres of iron and lead having the same mass are completely immersed in water. The density of lead is greater than that of iron. If the apparent loss of weight is $w_{1}$ for the iron sphere and $w_{2}$ for the lead sphere,then the ratio $\frac{w_{1}}{w_{2}}$ is:

$A$ small metal sphere of density $\varrho$ is dropped from height $h$ into a jar containing liquid of density $\sigma$ $(\sigma > \varrho)$. The maximum depth up to which the sphere sinks is (Neglect damping forces).