The pressure at half the depth of a lake is equal to two-third pressure at the bottom of the lake. So the depth 'h' of the lake is ($\rho$ = density of water in the lake, $g$ = acceleration due to gravity, $P_0$ = atmospheric pressure).

A spherical object is falling under gravity through a viscous fluid. The sphere attains the terminal velocity when

A piston of cross-sectional area $2.5 \times 10^{-2}\ \text{m}^2$ is used in a hydraulic lift to exert a force of $250\ \text{N}$ on water. The cross-sectional area of the other piston which supports a car of mass $3000\ \text{kg}$ is ($g = 9.8\ \text{m/s}^2$)

Two spherical black bodies of radii $R_1$ and $R_2$ having surface temperature $T_1$ and $T_2$ respectively, radiate the same power. The ratio of $R_1$ to $R_2$ will be