An AC voltage $$V=20 \sin 200 \pi t$$ is applied to a series LCR circuit which drives a current $$I=10 \sin \left(200 \pi t+\frac{\pi}{3}\right)$$. The average power dissipated is:

The mass of the moon is $$\frac{1}{144}$$ times the mass of a planet and its diameter is $$\frac{1}{16}$$ times the diameter of a planet. If the escape velocity on the planet is $$v$$, the escape velocity on the moon will be :

The output of the given circuit diagram is -

Two blocks of mass $$2 \mathrm{~kg}$$ and $$4 \mathrm{~kg}$$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $$4.0 \times 10^{-5} \mathrm{~m}$$ and Young's modulus of the metal is $$2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$$. The longitudinal strain developed in the wire is $$\frac{1}{\alpha \pi}$$. The value of $$\alpha$$ is _________. [Use $$g=10 \mathrm{~m} / \mathrm{s}^2$$]