The pressure of confined air is $p$. If the atmospheric pressure is $P$,then

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends a $90^o$ angle at the centre. The radius joining their interface makes an angle $\alpha$ with the vertical. The ratio $\frac{d_1}{d_2}$ is

If a vessel containing a fluid of density $\rho$ up to height $h$ is accelerated vertically downwards with acceleration $a_0$,then the pressure by the fluid at the bottom of the vessel is given by the equation ........ ($p_0$ denotes the atmospheric pressure and $g$ denotes the acceleration due to gravity).

Define relative density of a substance.

$A$ spherical marble of radius $1 \, cm$ is stuck in a circular hole of radius slightly smaller than its own radius (for calculation purpose,both can be taken same) at the bottom of a bucket filled with water up to a height of $10 \, cm$. If the mass of the marble is $20 \, g$,then the net force on the marble due to water is close to:

Find the depth of a lake at which the density of water is $1\%$ greater than at the surface. Given the compressibility of water $K = 50 \times 10^{-6} \text{ atm}^{-1}$. (Take $1 \text{ atm} = 10^5 \text{ Pa}$) (in $\text{ km}$)