The osmotic pressure of a $5\% \, w/v$ solution of cane sugar at $150 \, ^\circ C$ is ......... $atm$.

$A$ stone is dropped in a quiet lake and it is observed that waves move in circles. If the radius of a circular wave increases at the rate of $2 \text{ cm/sec}$,then the rate of increase in its area at the instant when its radius is $10 \text{ cm}$,is (in $\text{cm}^2/\text{sec}$): (in $\pi$)

In adiabatic compression,the decrease in volume is associated with

Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of the centre of mass of the system will be

The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is . . . . . . $\mathring{A}$ (radius of the first orbit of hydrogen atom $= 0.53 \ \mathring{A}$).

When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column, and the temperature remains constant while surface tension is neglected, what is the depth of the lake (in $m$)?