A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 6 J then total kinetic energy of the disc is

In potentiometer experiment, cells of e.m.f. $E_1$ and $E_2$ are connected in series $\left(E_1>E_2\right)$ the balancing length is 80 cm of the wire. If the polarity of $E_2$ is reversed, the balancing length becomes 20 cm. The ratio $\mathrm{E}_1 / \mathrm{E}_2$ is

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