The ratio of radii of gyration of a circular ring and circular disc of the same mass and radius, about an axis passing through their centres and perpendicular to their planes is

Two wires carrying currents $$5 \mathrm{~A}$$ and $$2 \mathrm{~A}$$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $$3 \mathrm{~A}$$ is situated outside the loop. The value of $$\oint \overrightarrow{\mathrm{B}} \overrightarrow{\mathrm{d} l}$$ around the loop is ( $$\mu_0=$$ permeability of free space, $$\overrightarrow{\mathrm{d} l}$$ is the length of the element on the Amperion loop)

A particle is suspended from a vertical spring which is executing S.H.M. of frequency $$5 \mathrm{~Hz}$$. The spring is unstretched at the highest point of oscillation. Maximum speed of the particle is $$(\mathrm{g} =10 \mathrm{~m} / \mathrm{s}^2)$$

Photoelectrons are emitted when photons of energy $$4.2 ~\mathrm{eV}$$ are incident on a photosensitive metallic sphere of radius $$10 \mathrm{~cm}$$ and work function $$2.4 ~\mathrm{eV}$$. The number of photoelectrons emitted before the emission is stopped is

$$\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9\right.$$ SI unit; $$\left.\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right]$$