A $600 \mathrm{g}$ of a solid cube having an edge length of $10 \mathrm{cm}$, floats in water. How much volume of the cube is inside water? (Given the density of water $={10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$)

In the shown figure, the pressure at points $A$ and $B$ are respectively $P_A$ and $P_B$. Prove that pressure at point $C$ is $\left(\frac{P_A+P_B}{2}\right)$.

How much energy is released when $8$ identical water drops each of radius $0.5\mathrm{cm}$ combine to form one big drop? If the energy is converted to kinetic energy, find the velocity of the big drop.

[Surface tension of water $=0.07 \mathrm{N} {\mathrm{m}}^{-1}$]

(i) A U-tube contains water and methylated spirit separated by mercury as shown below. What is the specific gravity of spirit?

(ii) In the above case if $10 \text{cm}$ of water and spirit each are further poured in the respective arms, find the difference of mercury levels in the two arms?

(i) Distinguish between streamline flow and turbulent flow.

(ii) Show that Bernoulli's equation is same as the equation due to Pascal's law in presence of gravity, if a liquid or a gas is at rest.

Explain why

(i) Mercury does not wet glass

(ii) The hair of a paint brush cling together when taken out of water

(iii) Heavier drops flatten and are not spherical in shape.