In an a.c. circuit with pure capacitance ' C ' and a.c. source $E=E_0 \sin \omega t$, the equation of instantaneous current is given by

Radius of curved road is ' $R$ ', width of road is ' $b$ '. The outer edge of road is raised by ' $h$ ' with respect to inner edge so that a car with velocity ' $V$ ' can pass safe over it, then value of ' $h$ ' is ( $\mathrm{g}=$ acceleration due to gravity)

A polyatomic gas is compressed to $\left(\frac{1}{8}\right)^{\text {th }}$ of its volume adiabatically. If its initial pressure is $\mathrm{P}_0$, its new pressure will be [Given, $\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4}{3}$ ]

A particle is executing linear S.H.M. starting from mean position. The ratio of the kinetic energy to the potential energy of the particle at a point of half the amplitude is