Force between two point charges $$q_1$$ and $$q_2$$ placed in vacuum at '$$r$$' cm apart is $$F$$. Force between them when placed in a medium having dielectric constant $$K=5$$ at '$$r / 5$$' $$\mathrm{cm}$$ apart will be:

A body of mass $$2 \mathrm{~kg}$$ begins to move under the action of a time dependent force given by $$\vec{F}=\left(6 t \hat{i}+6 t^2 \hat{j}\right) N$$. The power developed by the force at the time $$t$$ is given by:

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 :