The increase in the pressure required to decrease the volume ( $\Delta V$ ) of water is $6.3 \times 10^7 \mathrm{~N} / \mathrm{m}^2$. The percentage decrease in the volume is $\_\_\_\_$ .

(Bulk modulus of water $=2.1 \times 10^9 \mathrm{~N} / \mathrm{m}^2$.)

A string $A$ of length 0.314 m and Young's modulus $2 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$ is connected to another string $B$ of length and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg . The net change in length of the combination is $\_\_\_\_$ mm.

(radius of both the strings is 0.2 mm and acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ ) (Mass of both strings is to be neglected as compared to the mass of load)

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha \pi \times 10^{-4}$ J. The value of $\alpha$ is _________. (Take $\pi = 3.14$)

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m³ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take g = 10 m/s²)