The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength \(491\, nm\) is \(0.710\, V\). When the incident wavelength is changed to a new value, the stopping potential is \(1.43\, V\). The new wavelength is ....... \(nm.\)

At a certain depth "\(d\)" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height \(3\,R\) above earth surface. Where \(R\) is Radius of earth (Take \(R =6400\,km\) ). The depth \(d\) is equal to \(............\,km\)

Given below are two statements:
Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t. to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference.
In the light of the above statements,choose the correct answer from the options given below:

The voltage across the \(10\, \Omega\) resistor in the given circuit is \(x\) volt. The value of \('x'\) to the nearest integer is..........

For three low density gases \(A, B, C\) pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point ' \(K\) ' is \(...........\,{}^{\circ}\,C\)

A sinusoidal voltage \(V(t)=210\,\sin 3000 t\) volt is applied to a series \(LCR\) circuit in which \(L =10\) \(mH , C =25 \mu F\) and \(R =100 \Omega\). The phase difference \((\Phi)\) between the applied voltage and resultant current will be

A regular polygon of \(6\) sides is formed by bending a wire of length \(4 \pi\) meter. If an electric current of \(4 \pi \sqrt{3} \mathrm{~A}\) is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be \(x \times 10^{7} \mathrm{~T}\). The value of \(\mathrm{x}\) is ______.

Potential energy (V) versus distance (x) is given by the graph, Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.

The current in an inductor is given by \(\mathrm{I}=(3 \mathrm{t}+8)\) where \(t\) is in second. The magnitude of induced emf produced in the inductor is \(12 \mathrm{mV}\). The selfinductance of the inductor _______ \(\mathrm{mH}\).

An electromagnetic wave of frequency \(1\times10^{14}\, hertz\) is propagating along \(z-\) axis. The amplitude of electric field is \(4\, V/m\) . lf \({\varepsilon_0}=\, 8.8\times10^{-12}\, C^2/Nm^2\) , then average energy density of electric field will be:

A particle is subjected two simple harmonic motions as :
\(\mathrm{x}_1=\sqrt{7} \sin 5 \mathrm{tcm}\)
and \(x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}\)
where x is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(\mathrm{x} \times 10^{-2} \mathrm{~ms}^{-2}\). The value of x is :