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 $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$)

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _________ J.

The potential energy of a particle of mass $$4 \mathrm{~kg}$$ in motion along the x-axis is given by $$\mathrm{U}=4(1-\cos 4 x)$$ J. The time period of the particle for small oscillation $$(\sin \theta \simeq \theta)$$ is $$\left(\frac{\pi}{K}\right) s$$. The value of $$\mathrm{K}$$ is _________.

An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about _______ W.