A tub is filled with water and a wooden cube $10\ \text{cm} \times 10\ \text{cm} \times 10\ \text{cm}$ is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by $3.87$ cm. The mass of the metal coin is ________ gram.

(Take water density as $1\ \text{g/cm}^3$ and density of wood as $0.4\ \text{g/cm}^3$)

A soap bubble of surface tension $0.04 \mathrm{~N} / \mathrm{m}$ is blown to a diameter of 7 cm . If $(15000-x) \mu \mathrm{J}$ of work is done in blowing it further to make its diameter 14 cm , then the value of $x$ is $\_\_\_\_$ .

$$ (\pi=22 / 7) $$

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$ coalesce to form a bigger drop. The terminal velocity of bigger drop is

$\_\_\_\_$ $\mathrm{cm} / \mathrm{s}$.

A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$, given by $t=A \rho^a r^b \eta^c \sigma^d$, where $A$ is a constant and $a, b, c$ and $d$ are integers. The value of $\frac{b+c}{a+d}$ is $\_\_\_\_$ .