A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\frac{l}{3}$ distance from the top is $\left( \frac{W}{A} + \frac{2}{\gamma} \frac{w}{A} \right)$, where $A$ is the cross sectional area of the wire. The value of $\gamma$ is ________.

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

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