$A$ liquid is kept in a closed vessel. If a glass plate (negligible mass) with a small hole is kept on top of the liquid surface,then the vapour pressure of the liquid in the vessel is

$A$ spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius $r$ with time $t$ is ... (where $k$ is a positive constant)

$A$ motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver $n$-times the water through the same pipe in the same time, the power of the motor must be increased as follows:

$A$ bubble of radius $R$ in water of density $\rho$ is expanding uniformly at speed $v$. Given that water is incompressible,the kinetic energy of water being pushed is

The phenomenon of lowering the freezing point of water by the application of pressure is known as

When a soap bubble of radius $0.2 \ mm$ is charged,it experiences an outward electrostatic pressure of magnitude $\frac{\sigma^2}{2 \varepsilon_0}$,where $\sigma = 20 \ \mu C \ m^{-2}$ is the surface charge density. If the excess pressure inside the soap bubble due to the surface tension is same as this electrostatic pressure,then the surface tension of the soap solution is (Given: $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$)