A group of lamps having total power rating of $$1000 \mathrm{~W}$$ is supplied by an AC voltage of $$E=200 \sin \left(310 t+60^{\circ}\right)$$, the rms value of current flowing through the circuit is

At a particular angular frequency, the reactance of capacitor and that of inductor is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

A metal disc of radius $$R$$ rotates with an angular velocity $$\omega$$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $$B$$ acting perpendicular to the plane of the disc. The magnitude of induced emf between the rim and axis of the disc is

A mass $$M$$ is suspended from a light spring. An additional mass $$M_1$$ added extends the spring further by a distance $$x$$. Now, the combined mass will oscillate on the spring with period $$T=$$