A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is

A solid sphere of radius $r$ is floating at the  interface of two immiscible liquids of densities $\rho_1$ and $\rho_2\,\, (\rho_2 > \rho_1),$ half of its volume lying in each. The height of the upper liquid column from the interface of the two liquids is $h.$ The force exerted on the sphere by the upper liquid is $($ atmospheric pressure $= p_0\,\,\&$ acceleration due to gravity is $g) $

A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance $l $ and $h$ are shown there. After some time the coin falls into the water. Then

Water is pumped from a depth of $10 $ $m$ and delivered through a pipe of cross section $10^{-2}$ $m^2$. If it is needed to deliver a volume of $10^{-1} $ $m^3$ per second the power required will be ........ $kW$

A hemispherical bowl just floats without sinking in a liquid of density $1.2 × 10^3kg/m^3$. If outer diameter and the density of the bowl are $1 m$  and $2 × 10^4 kg/m^3$ respectively, then the inner diameter of the bowl will be........ $m$

A homogeneous solid cylinder of length $L$$(L < H/2)$. 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 fig. The lower density liquid is open to atmosphere having pressure ${P_0}$. Then density $D$  of solid is given by