If $$\epsilon_{\mathrm{o}}$$ is the permittivity of free space and $$\mathrm{E}$$ is the electric field, then $$\epsilon_{\mathrm{o}} \mathrm{E}^2$$ has the dimensions :

Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of $$\mathrm{A}$$ is $$3 v$$, the speed of $$\mathrm{B}$$ will be :

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be ̱________ to ________ times of its initial length if the water is to be boiled in 15 minutes.

A diatomic gas $$(\gamma=1.4)$$ does $$100 \mathrm{~J}$$ of work in an isobaric expansion. The heat given to the gas is :