$A$ $U$-tube containing a liquid moves with a horizontal acceleration $a$ along a direction joining the two vertical limbs. The separation between these limbs is $d$. The difference in their liquid levels is

The relative density of Kerosene is $0.8$. Find its density. (in $kg/m^3$)

In the figure, chamber $A$ contains a gas, a movable chamber $B$ is placed on top of the gas and it contains $n$ metal balls. The weight of chamber $B$ and the balls is supported by the gas. Chamber $C$ is a vacuum. Let the gas be in equilibrium at pressure $P$. Let $P^{\prime}$ be the pressure if one of the balls is taken away. Find $(P-P^{\prime}) / P$.

In making an alloy,a substance of specific gravity $s_1$ and mass $m_1$ is mixed with another substance of specific gravity $s_2$ and mass $m_2$; then the specific gravity of the alloy is

Mountaineers suffer from nose bleeding (epistaxis) at higher altitudes. Explain.

Two communicating vessels contain mercury. The diameter of one vessel is $n$ times larger than the diameter of the other. $A$ column of water of height $h$ is poured into the left vessel. The mercury level will rise in the right-hand vessel ($s =$ relative density of mercury and $\rho =$ density of water) by