A small solid ball is dropped from a height above the free surface of a liquid. It strikes the surface of the liquid at $t = 0$. The density of the material of the ball is $500\  kg/m^3$ and that of liquid is $1000\  kg/m^3$ If the ball comes momeritariiy at rest at $t = 2\  sec$ then initial height of the ball from surface of liquid was ….. $m$ (neglect viscosity)

A cube of ice floats partly in water and partly in kerosene oil. The radio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil $=0.8$, specific gravity of ice $=0.9$ )

A very large block of ice of the size of a volleyball court and of uniform thickness of $8 \,m$ is floating on water. A person standing near its edge wishes to fetch a bucketful of water using a rope. The smallest length of rope required for this is about …………… $m$

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

A vertical triangular plate $ABC$ is placed inside water with side $BC$ parallel to water surface as shown. The force on one surface of plate by water is (density of water is $\rho $ and atmospheric pressure $P_0$ )