Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis $$A B$$ as shown in figure is $$\sqrt{8 / x}$$. The value of $$x$$ is :

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

A simple pendulum doing small oscillations at a place $$R$$ height above earth surface has time period of $$T_1=4 \mathrm{~s}$$. $$\mathrm{T}_2$$ would be it's time period if it is brought to a point which is at a height $$2 \mathrm{R}$$ from earth surface. Choose the correct relation [$$\mathrm{R}=$$ radius of earth] :

Match List I with List II :

(Where $$\mathrm{a}=$$ radius of planet orbit, $$\mathrm{r}=$$ radius of planet, $$\mathrm{M}=$$ mass of Sun, $$\mathrm{m}=$$ mass of planet)

Choose the correct answer from the options given below :