$A$ sphere of material of relative density $8$ has a concentric spherical cavity and just sinks in water. If the radius of the sphere is $2 \ cm$,then the volume of the cavity is

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 cylinders of same cross-section and length $L$ but made of two materials of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with a length $L/2$ above the surface of the liquid. If $d_1 > d_2$,then:

$A$ $0.5 \,kg$ block of brass (density $=8 \times 10^3 \,kg \,m^{-3}$) is suspended from a string. What is the tension in the string if the block is completely immersed in water? $(g=10 \,ms^{-2})$

$A$ homogeneous solid cylinder of length $L$ $(L < H/2)$ and cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to the atmosphere having pressure $P_0$. Then,the density $D$ of the solid is given by:

What is buoyant force?