A solid metallic sphere of radius ' $R$ ' having moment of inertia '$I$' about diameter is melted and recast into a solid disc of radius ' $r$ ' of a uniform thickness. The moment of inertia of a disc about an axis passing through its edge and perpendicular to its plane is also equal to '$I$'. The ratio $\frac{r}{R}$ is

In young's double slit experiment, the $\mathrm{n}^{\text {th }}$ maximum of wavelength $\lambda_1$ is at a distance of $y_1$ from the central maximum. When the wavelength of the source is changed to $\lambda_2,\left(\frac{\mathrm{n}}{3}\right)^{\text {th }}$ maximum is at a distance of $y_2$ from its central maximum. The ratio $\frac{y_1}{y_2}$ is

For a particle in uniform circular motion

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