The work done by a gas molecule in an isolated system is

given by, $$W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha kT}}}}$$, where x is the displacement, k is the Boltzmann constant and T is the temperature. $$\alpha$$ and $$\beta$$ are constants. Then the dimensions of $$\beta$$ will be :

Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :

If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The value of $$\beta$$ will be :

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :