A metallic body of material with density of $8000\  kg/m^3$ has a cavity inside. A spring balance shows its mass to be $10.0\  kg$ in air and $7.5\  kg$ when immersed in water. The ratio of the volume of the cavity to the volume of the material of the body must be

A block of ice floats in an oil in a vessel when the ice melts, the level of oil will …………..

A spherical ball of radius $r$ and relative density $0.5$ is floating in equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that whole of it is just immersed in water is : (where $\rho $ is the density of water)

An empty balloon weighs $1\, g$. The balloon is filled with water to the neck and tied with  a massless thread. The weight of balloon alongwith water is $101\, g$. The balloon filled with  water is weighed when fully immersed. Then, its weight in water is …… $g$

A metallic block of density $5\,gm \,cm^{-3}$ and having dimensions $5 cm × 5 cm × 5 cm$ is weighed in water. Its apparent weight will be