Three liquids have same surface tension and densities $\rho_1$, $\rho_2$ and $\rho_3$ ($\rho_1 < \rho_2 < \rho_3$). In three identical capillaries rise of liquid is same. The corresponding angle of contact $\theta_1$, $\theta_2$ and $\theta_3$ are related as

The excess pressure inside the first soap bubble of radius $R_1$ is three times that inside the second soap bubble of radius $R_2$. The ratio of volumes of the first to second bubble is

The ratio of the thermal conductivity of two rods of different materials is 6:5. The two rods of same area of cross section and same thermal resistance will have the length in the ratio

A black rectangular surface of area A emits energy E per second at $127^\circ$C. If length and breadth is reduced to half of initial value and temperature is raised to $527^\circ$C then energy emitted becomes