A string \(2.0\, m\) long and fixed at its end is driven by a \(240\, Hz\) vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

A given object takes \(n\) times the time to slide down \(45^{\circ}\) rough inclined plane as it takes the time to slide down an identical perfectly smooth \(45^{\circ}\) inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is _______.

A block of mass \(0.1\, kg\) is connected to an elastic spring of spring constant \(640\, Nm^{-1}\) and oscillates in a damping medium of damping constant \(10^{-2}\, kg\,s^{-1}\) . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to ..... \(s\)

An electron in a hydrogen atom revolves around its nucleus with a speed of \(6.76 \times 10^6\,ms ^{-1}\) in an orbit of radius \(0.52\,\mathring A\). The magnetic field produced at the nucleus of the hydrogen atom is \(......T\).

In the given circuit, the current through zener diode is......\(mA\)

Assume that protons and neutrons have equal masses. Mass of a nucleon is \(1.6 \times 10^{-27}\,kg\) and radius of nucleus is \(1.5 \times 10^{-15} A ^{1 / 3}\,m\). The approximate ratio of the nuclear density and water density is \(n \times 10^{13}\). The value of \(n\) is \(.................\)

Equivalent resistance between the adjacent corners of a regular \(n\)-sided polygon of uniform wire of resistance \(R\) would be:

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to \(\operatorname{arc} \mathrm{AB}\) to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?

The distance between object and its \(3\) times magnified virtual image as produced by a convex lens is \(20 \mathrm{~cm}\). The focal length of the lens used is _______ \(\mathrm{cm}\).

An observer is riding on a bicycle and moving towards a hill at \(18\,km\,h ^{-1}\). He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is \(640\,\,Hz\) and velocity of the sound in air is \(320\,m / s\), the beat frequency between the two sounds heard by observer will be \(...Hz\).