Two cells of emf 2E and E with internal resistance r₁ and r₂ respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes zero is

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms^-1 goes up an inclined plane which makes an angle of 30$$^\circ$$ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?

Two particles A and B of equal masses are suspended from two massless springs of spring constants K₁ and K₂ respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is