$1000$ small water drops,each of radius $r$ and charge $q$,coalesce together to form one large spherical drop. The potential of the big drop is larger than that of the smaller drop by a factor of:

In a cylinder provided with a piston, air is under pressure $P_1$ at a constant temperature $t$. $A$ soap bubble with radius $r$ and surface tension $T$ is lying inside the cylinder. To reduce the radius of the soap bubble to half, the required air pressure inside the cylinder is

In a water tank,an air bubble rises from the bottom to the top surface of the water. If the depth of the water in the tank is $7.28 \ m$ and atmospheric pressure is $10 \ m$ of water,then the ratio of the radii of the bubble at the bottom of the tank and at the top surface of the water is (Temperature of the water in the tank is constant).

The surface tension of a soap bubble is $0.03 \text{ N/m}$. The work done in increasing the diameter of the bubble from $2 \text{ cm}$ to $6 \text{ cm}$ is $\alpha \times 10^{-4} \text{ J}$. The value of $\alpha$ is . . . . . . (Take $\pi = 3.14$).

The pressure inside a soap bubble $A$ is $1.01 \text{ atm}$ and that in a soap bubble $B$ is $1.02 \text{ atm}$. The ratio of the volume of $A$ to that of $B$ is

The work done in breaking a drop of liquid of radius $R$ (Surface tension $T$) into $64$ equal drops is