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 bubble to second bubble is

Determine the ratio of surface energy of $1$ large drop to $1$ small drop, if $1000$ small drops combined to form $1$ large drop.

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