Two massless springs of spring constant $$\mathrm{K}_1$$ and $$\mathrm{K}_2$$ are connected one after the other forming a single chain, suspended vertically and certain mass is attached to the free end. If '$$e_1$$' and '$$e_2$$' are their respective extensions and '$$\mathrm{f}$$' is their stretching force, the total extension produced is

The time taken by a particle executing simple harmonic motion of period '$$\mathrm{T}$$', to move from the mean position to half the maximum displacement is

Using Bohr's model, the orbital period of electron in hydrogen atom in the $$\mathrm{n}^{\text {th }}$$ orbit is $$\left(\varepsilon_0=\right.$$ permittivity of vacuum, $$\mathrm{h}=$$ Planck's constant, $$\mathrm{m}=$$ mass of electron, $$\mathrm{e}=$$ electronic charge)

A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved further apart by pulling them by means of insulating handles, then