When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $$\mathrm{v}_1$$ and $$\mathrm{v}_2$$ respectively. The ratio $$\mathrm{v}_1: \mathrm{v}_2$$ is

A simple pendulum of length $$2 \mathrm{~m}$$ is given a horizontal push through angular displacement of $$60^{\circ}$$. If the mass of bob is 200 gram, the angular velocity of the bob will be (Take Acceleration due to gravity $$=10 \mathrm{~m} / \mathrm{s}^2$$ ) $$\left(\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2\right)$$

The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number '$$n$$' as

If the frequency of the input voltage is $$50 \mathrm{~Hz}$$, applied to a (a) half wave rectifier and (b) full wave rectifier. The output frequency in both cases is respectively