$A$ person of height $1.65 \,m$ is standing upright. The additional external force required by a blood vessel of length $1 \,cm$, diameter $1 \,mm$ at the feet to balance the pressure compared to a similar blood vessel in the head is (Density of blood $= 1.1 \times 10^3 \,kg \,m^{-3}$, $g = 10 \,ms^{-2}$) (in $\,N$)

Density of ice is $\rho$ and that of water is $\sigma$. What will be the decrease in volume when a mass $M$ of ice melts?

The figure shows a container filled with a liquid of density $\rho$. Four points $A, B, C$ and $D$ lie on the diametrically opposite points of a circle as shown. Points $A$ and $C$ lie on a vertical line,and points $B$ and $D$ lie on a horizontal line. Which of the following statements is incorrect? (Here,$p_A, p_B, p_C, p_D$ are the absolute pressures at the respective points.)

$A$ tank $5 \,m$ high is half filled with water and then is filled to the top with oil of density $0.85 \,g/cm^3$. The pressure at the bottom of the tank,due to these liquids is ........ $g/cm^2$.

Two points $A$ and $B$ are at the same depth in a liquid at rest. Then the pressure on them $P_A$ ........... $P_B$.

Three liquids of equal masses are taken in three identical cubical vessels $A$,$B$,and $C$. Their densities are $\rho_{A}$,$\rho_{B}$,and $\rho_{C}$ respectively,where $\rho_{A} < \rho_{B} < \rho_{C}$. The force exerted by the liquid on the base of the cubical vessel is