A string of area of cross-section $$4 \mathrm{~mm}^{2}$$ and length $$0.5 \mathrm{~m}$$ is connected with a rigid body of mass $$2 \mathrm{~kg}$$. The body is rotated in a vertical circular path of radius $$0.5 \mathrm{~m}$$. The body acquires a speed of $$5 \mathrm{~m} / \mathrm{s}$$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _________ $$ \times 10^{-5}$$.

(use Young's modulus $$10^{11} \mathrm{~N} / \mathrm{m}^{2}$$ and $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$)

The diameter of an air bubble which was initially $$2 \mathrm{~mm}$$, rises steadily through a solution of density $$1750 \mathrm{~kg} \mathrm{~m}^{-3}$$ at the rate of $$0.35 \,\mathrm{cms}^{-1}$$. The coefficient of viscosity of the solution is _________ poise (in nearest integer). (the density of air is negligible).

In an experiment to determine the Young's modulus, steel wires of five different lengths $$(1,2,3,4$$, and $$5 \mathrm{~m})$$ but of same cross section $$\left(2 \mathrm{~mm}^{2}\right)$$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $$x \times 10^{11} \,\mathrm{Nm}^{-2}$$, then the value of $$x$$ is __________.

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ___________.