A particle at rest starts moving with constant angular acceleration $$4 ~\mathrm{rad} / \mathrm{s}^2$$ in circular path. At what time the magnitudes of its tangential acceleration and centrifugal acceleration will be equal?

If the end correction of an open pipe is $$0.8 \mathrm{~cm}$$, then the inner radius of that pipe is

The mutual inductance (M) of the two coils is $$3 ~\mathrm{H}$$. The self inductances of the coils are $$4 ~\mathrm{H}$$ and $$9 ~\mathrm{H}$$ respectively. The coefficient of coupling between the coils is

A particle is vibrating in S.H.M. with an amplitude of $$4 \mathrm{~cm}$$. At what displacement from the equilibrium position is its energy half potential and half kinetic?