The de Broglie wavelength of an electron having kinetic energy \(E\) is \(\lambda\). If the kinetic energy of electron becomes \(\frac{E}{4}\), then its de-Broglie wavelength will be :

Given a charge \(q\), current I and permeability of vacuum \(\mu_0\). Which of the following quantity has the dimension of momentum?

In a circuit for finding the resistance of a galvanometer by half deflection method, a  \(6\,V\)  battery and a high resistance of  \(11\,k\Omega \)  are used. The figure of merit of the galvanometer \(60\,\mu A/\)  division. In the absence of shunt resistance, the galvanometer produces a deflection of  \(\theta = 9\)  divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of \(\theta /2 ,\)  is closest to ..................  \(\Omega\)

A long solenoid of radius \(\mathrm{R}\) carries a time \((t)-\)dependent current \(\mathrm{I}(\mathrm{t})=\mathrm{I}_{0} \mathrm{t}(1-\mathrm{t})\). A ring of radius \(2 \mathrm{R}\) is placed coaxially near its middle. During the time interval \(0 \leq t \leq 1\), the induced current \(\left(\mathrm{I}_{\mathrm{R}}\right)\) and the induced \(\mathrm{EMF}\left(\mathrm{V}_{\mathrm{R}}\right)\) in the ring change as

The resistance of a conductor at \(15^{\circ} {C}\) is \(16\, \Omega\) and at \(100\, {C}\) is \(20\, \Omega\). What will be the temperature coefficient of resistance of the conductor?

A block of mass \(10\,kg\) is moving along \(x\)-axis under the action of force \(F=5 x\; N\). The work done by the force in moving the block from \(x =2\,m\) to \(4\,m\) will be ............\(J\).

A body \(A\) of mass \(\mathrm{m}\) is moving in a circular orbit of radius \(\mathrm{R}\) about a planet. Another body \(\mathrm{B}\) of mass \(\frac{\mathrm{m}}{2}\) collides with \(\mathrm{A}\) with a velocity which is half \(\left(\frac{\overrightarrow{\mathrm{v}}}{2}\right)\) the instantaneous velocity \(\overrightarrow{\mathrm{v}}\) of \(\mathrm{A}\) The collision is completely inelastic. Then, the combined body

A metal surface is illuminated by a radiation of wavelength \(4500 \; \mathring A\). The ejected photo-electron enters a constant magnetic field of \(2 \; mT\) making an angle of \(90^{\circ}\) with the magnetic field. If it starts revolving in a circular path of radius \(2 \; mm\), the work function of the metal is approximately ............. \(eV\)