The excess pressure inside the first soap bubble is three times that inside the second bubble then, the ratio of volume of the first to the second bubble will be

The work done in blowing a soap bubble of radius $0.2\,m$, given that the surface tension of soap solution is $60\times10^{-3}\, N/M$ is

A spherical solid ball of volume $V$ is made of a material of density ${\rho _1}$ . It is falling through a liquid of density ${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$. Assume that the liquid  applies a viscous force on the ball that is propoertional to the square of its speed $v$ , i.e., ${F_{{\rm{viscous}}}} =  – k{v^2}\left( {k > 0} \right)$. Then terminal speed of the bal is

A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$. The fraction of volume immersed in the liquid will be :-

Two drops of equal radius are falling through air with a steady velocity of $5\,cm/s$. If the two drops coalesce, then its terminal velocity will be