A vessel completely filled with water has two holes ' P ' and ' Q ' at depths ' 2 h ' and ' 8 h ' from the top respectively. Hole ' P ' is square of side ' $a$ ' and hole ' $Q$ ' is a circle of radius ' $r$ '. The water flowing out per second from both the holes is same, then side ' $a$ ' of hole ' $P$ ' is

A spherical liquid drop splits in to 729 identical spherical drops. If $E$ is the surface energy of the original drop and $U$ is the total surface energy of resulting drops, then $\frac{E}{U}=\frac{1}{x}$. The value of $x$ is

The work done in splitting a water drop of radius R into 64 droplets is ( $\mathrm{T}=$ surface tension of water)

Under isothermal conditions, two soap bubbles of radii $r_1$ and $r_2$ coalesce to form a big drop. The radius of the big drop is