$A$ sphere of solid material of relative density $9$ has a concentric spherical cavity and floats just submerged in water. If the radius of the sphere is $R$,then the radius of the cavity $(r)$ is related to $R$ as:

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:

$A$ solid sphere of specific gravity $27$ has a concentric spherical cavity and it just sinks in water. The ratio of the cavity radius to the outer radius of the sphere is

$A$ block of wood is floating on water at $0^{\circ} C$ with volume $V_0$ above water. When the temperature of water increases from $0^{\circ} C$ to $10^{\circ} C$,the change in the volume of the block that is above water is best described schematically by which graph?

The reading of a spring balance when a block is suspended from it in air is $60\,N$. This reading changes to $40\,N$ when the block is immersed in water. The specific density (relative density) of the block is:

Two cubes of size $1.0 \ m$ sides,one of relative density $0.60$ and another of relative density $1.15$ are connected by a weightless wire and placed in a large tank of water. Under equilibrium,the lighter cube will project above the water surface to a height of ........ $cm$.