A particle performs simple harmonic motion with a period of \(2\) second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is \(\frac{1}{ a } s .\) The value of \('a'\) to the nearest integer is.........

A thin prism \(P_1\) with an angle \(6^{\circ}\) and made of glass of refractive index \(1.54\) is combined with another prism \(P _2\) made from glass of refractive index \(1.72\) to produce dispersion without average deviation. The angle of prism \(P_2\) is \(........{}^{\circ}\)

Identify the pair of physical quantities that have same dimensions

A parallel beam of monochromatic light of wavelength \(5000 \mathring A\) is incident normally on a single narrow slit of width \(0.001 \mathrm{~mm}\). The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of______________(degree).

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of \(\frac{1}{\theta}\) vs the resistance \((R)\) of the resistance box is shown in the figure. The figure of merit of the galvanometer is _______ \(\times 10^{-1} \mathrm{~A} /\) division. [The source has emf 2V]

An electron with speed \(v\) and a photon with speed \(c\) have the same \(de-Broglie\) wavelength. If the kinetic energy and momentum of electron are \(E_{ e }\) and \(pe _{ e }\) and that of photon are \(E _{ ph }\) and \(p _{ ph }\) respectively. Which of the following is correct?

A straight wire \(AB\) of mass \(40\,g\) and length \(50\,cm\) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \(0.40\,T\) as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........\(A\). (Take \(g=10\,ms ^{-2}\) ).

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity \(3\, m / s\) (as shown in figure). Maximum height with respect to the initial position covered by it will be \(...........cm\).

A particle moving in the \(xy\) plane experiences a velocity dependent force \(\overrightarrow{ F }= k \left( v _{ y } \hat{ i }+ v _{ x } \hat{ j }\right),\) where \(v _{ x }\) and \(v _{ y }\) are the \(x\) and \(y\) components of its velocity \(\overrightarrow{ v } .\) If \(\overrightarrow{ a }\) be the acceleration of the particle, then which of the following statements is true for the particle\(?\)

An \(npn\) transistor operates as a common emitter amplifier, with a power gain of \(60\, dB\). The input circuit resistance Is \(100\,\Omega \) and the output load resistance is \(10 \,k\,\Omega \). the common emitter current gain \(\beta \) is

The equation of a plane progressive wave is given by \(y = 5\cos\pi\left(200t - \dfrac{x}{150}\right)\) where \(x\) and \(y\) are in cm and \(t\) is in second. The velocity of the wave is _______ m/s.

For the given circuit the current \(i\) through the battery when the key in closed and the steady state has been reached is .....\(A\)