A spherical drop of liquid splits into $1000$ identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation). $u_f / u_i = (10/x)$. Then value of $x$ is

The surface of water in a water tank of cross-section area $750$ cm$^2$ on the top of a house is $h$ m above the tap level. The speed of water coming out through the tap of cross-section area $500$ mm$^2$ is $30$ cm/s. At that instant, $dh/dt$ is $y \times 10^{-3}$ m/s. The value of $y$ will be

What will be the ratio of rate of radiation of metal sphere at two different temperatures $T_1 = 527^\circ$C and $T_2 = 127^\circ$C

The coefficient of thermal conductivity of a metal rod depends on its