An air bubble of volume $50\, cm^3$ is formed at the bottom of a lake $47.6\, m$ deep. What will be its volume when it reaches the surface? (Atmospheric pressure $= 70\, cm$ of $Hg$ and density of $Hg = 13.6\, g/cm^3$)

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: $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$)

$A$ razor-blade floats on the surface of water contained in a glass. When the glass is gently shaken,the razor-blade sinks. Mark the incorrect statement.

$Assertion :$ $A$ thin stainless steel needle can float on a still water surface.
$Reason :$ Any object floats when the buoyancy force balances the weight of the object.

Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density $d$. The height of the liquid in one vessel is $h_1$ and that in the other vessel is $h_2$. The area of either base is $A$. The work done by gravity in equalizing the levels when the two vessels are connected is

$A$ pump motor is used to deliver water at a certain rate from a given pipe. To obtain twice as much water from the same pipe in the same time, the power of the motor has to be increased to: (in $\times$)