A metallic ring of radius R moves in a vertical plane in the presence of a uniform magnetic field B perpendicular to the plane of the ring. At any given instant of time its centre of mass moves with a velocity v while ring rotates in its COM frame with angular velocity ω as shown in the figure. The magnitude of induced e.m.f. between points O and P is

An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?

The relation between R and r (internal resistance of the battery) for which the power consumed in the external part of the circuit is maximum

A capacitor and resistor are connected with an A.C. source as shown in figure. Reactance of capacitor is X_C = 3W and resistance of resistor is 4Ω. Phase difference between current I and I₁ is

Find the stress at distance R/2 from centre in a uniformly charged non conducting sphere having radius R and charge density ρ.

The capacitor is initially uncharged. Find ratio of current through the 10 Ω resistance and through the 20 Ω resistance initially.

In the diagram below, light is incident on the interface between media 1 and 2 as shown and is totally reflected. The light is then also totally reflected at the interface between media 1 and 3, after which it travels in a direction opposite to its initial direction. The two interfaces are perpendicular. The refractive indices are related as

Which of the following transitions of He⁺ ion will give rise to spectral line which has same wavelength as some spectral line in hydrogen atom ?

Two imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the concentric spheres. When compared to the number of field lines N₁ going through the sphere of radius R, the number of electric field lines N₂ going through the sphere of radius 2R is

A radioactive sample contains two radioactive nucleus A and B having decay constant λ hr^–1 and 2λ hr^–1. Initially 20% of decay comes from A. How long (in hr) will it take before 50% of decay comes from A. [Take λ = ln 2]