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)

A motor cyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius ' $R$ ' metre. If the coefficient of friction between the wall and the tyres is ' $\mu_{\mathrm{s}}$ ', then the minimum speed required is ( $\mathrm{g}=$ acceleration due to gravity)

Two sound waves travelling in the same direction have displacement $\mathrm{y}_1=\mathrm{a} \sin (0.2 \pi \mathrm{x}-50 \pi \mathrm{t})$ and $\mathrm{y}_2=\mathrm{a} \sin (0.15 \pi \mathrm{x}-46 \pi \mathrm{t})$.

How many times, a listener can hear sound of maximum intensity in one second?