Diagram shows a jar filled with two non mixing liquids $1$ and $2$ having densities ${\rho _1}$ and ${\rho _2}$ respectively. A solid ball, made of a material of density ${\rho _3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${\rho _1}$ , ${\rho _2}$ and ${\rho _3}$ ?
${\rho _3} < {\rho _1} < {\rho _2}$
${\rho _1} < {\rho _3} < {\rho _2}$
${\rho _1} < {\rho _2} < {\rho _3}$
${\rho _1} > {\rho _3} > {\rho _2}$
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 $P_0$ )
A container of liquid release from the rest, on a smooth inclined plane as shown in the figure. Length of at the inclined plane is sufficient, and assume liquid finally equilibrium. Finally liquid surface makes an angle with horizontal ...... $^o$
A block of volume $V$ and of density $\sigma _b$ is placed in liquid of density $\sigma _l(\sigma _l > \sigma _b)$ , then block is moved upward upto a height $h$ and it is still in liquid. The increase in gravitational potential energy of the system is
A uniform cylinder of length $L$ and mass $M$ having crosssectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is
A ball of relative density $0.8$ falls into water from a height of $2$ $m$. The depth to which the ball will sink is ........ $ m$ (neglect viscous forces) :