Two stones of masses m and 3 m are whirled in horizontal circles, the heavier one in a radius $\left(\frac{\mathrm{r}}{3}\right)$ and lighter one in a radius r . The tangential speed of lighter stone is ' $n$ ' times the value of heavier stone. When the magnitude of centripetal force becomes equal the value of $n$ is

A $4 \mu \mathrm{~F}$ capacitor is charged to 10 V . The battery is then disconnected and a pure 10 mH coil is connected across the capacitor so that LC oscillations are set up. The maximum current in the coil is

An object of mass 0.2 kg executes simple harmonic oscillations along the x -axis with frequency of $\left(\frac{25}{\pi}\right) \mathrm{Hz}$. At the position $x=0.04 \mathrm{~m}$, the object has kinetic energy 1 J and potential energy 0.6 J . The amplitude of oscillation is

Two current carrying identical coils are kept as shown in figure. The magnetic field at centre ' O ' is ( N and R represent the number of turns and radius of each coil respectively, $\mu_0=$ permeability of free space)