$A$ wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When a certain amount of oil is poured into the bucket,it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is

$A$ leak-proof cylinder of length $1 \; m,$ made of a metal which has a very low coefficient of expansion,is floating vertically in water at $0^{\circ} C$ such that its height above the water surface is $20 \; cm.$ When the temperature of water is increased to $4^{\circ} C,$ the height of the cylinder above the water surface becomes $21 \; cm.$ The density of water at $T=4^{\circ} C,$ relative to the density at $T=0^{\circ} C,$ is close to

$A$ wooden piece floats half-submerged in a tub of water. If the system is transferred to a lift ascending with acceleration $a$,the wooden piece will:

$A$ block of iron contains a hollow cavity as shown below. The block weighs $6000 \,N$ in air and $4000 \,N$ in water. If the densities of iron and water are $6 \,g/cm^3$ and $1 \,g/cm^3$ respectively, then the volume of the cavity is (assume $g = 10 \,m/s^2$): (in $\,m^3$)

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:

$A$ cubical block of steel of each side equal to $l$ is floating on mercury in a vessel. The densities of steel and mercury are $\rho_s$ and $\rho_m$. The height of the block above the mercury level is given by: