Due to surface tension, the excess pressure inside a smaller drop is $9$ units. If $27$ smaller drops combine then excess pressure inside the bigger drop is

Two rain drops of same radius '$r$' falling with same terminal velocity '$V$' merge and form bigger drop of radius '$R$'. The terminal velocity of big drop is

A spherical ball of radius $1$ mm and density $10.5$ g/cc is dropped in glycerine of coefficient of viscosity $9.8$ poise and density $1.5$ g/cc. Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x}$ N. The value of $x$ is
(Given, $g = 9.8 \text{ m}/\text{s}^2$ and $\pi = \dfrac{22}{7}$)

A vessel contains oil (density $= 0.8 \text{ gm}/\text{cm}^3$) over mercury (density $= 13.6 \text{ gm}/\text{cm}^3$). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $\text{gm}/\text{cm}^3$ is