The work done in blowing a soap bubble of radius $R$ is $W_1$ at room temperature. Now the soap solution is heated. From the heated solution another soap bubble of radius 2 R is blown and the work done is $\mathrm{W}_2$. Then

Two soap bubbles having radii ' $r_1$ ' and ' $r_2$ ' has inside pressure ' $P_1$ ' and ' $\mathrm{P}_2$ ' respectively. If $\mathrm{P}_0$ is external pressure then ratio of their volume is

Two metal spheres are falling through a liquid of density $2.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ with the same uniform speed. The density of material of first sphere and second sphere is $11.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ and $8.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ respectively. The ratio of the radius of first sphere to that of second sphere is

A glass capillary of radius 0.35 mm is inclined at $60^{\circ}$ with the vertical in water. The height of the water column in the capillary is (surface tension of water $=7 \times 10^{-2} \mathrm{~N} / \mathrm{m}$, acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2, \cos 0^{\circ}=1, \cos 60^{\circ}=0.5$ )