In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V , what is the wavelength of the em-wave ?
(Given hc \(=1242 \mathrm{eVnm}\) where h is the Planck's constant and c is the speed of light in vaccum.)

The amplitude of wave disturbance propagating in the positive \(x\)-direction is given by \(y=\frac{1}{(1+x)^{2}}\) at time \(t=0\) and \(y=\frac{1}{1+(x-2)^{2}}\) at \(t=1\) s, where \(x\) and \(y\) are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be \(...\,{m} / {s}.\)

What should be the order of arrangement of de-Broglie wavelength of elelctron \(\left(\lambda_{{e}}\right)\), an \(\alpha-\) particle \(\left(\lambda_{\alpha}\right)\) and proton \(\left(\lambda_{p}\right)\) given that all have the same kinetic energy ?

Correct Bernoulli's equation is _______. (symbols have their usual meaning)

A ball of mass \(0.5 \; kg\) is dropped from the height of \(10 \; m\). The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is \(\dots \; m\). (Use \(g =10 \; m / s ^{2}\)).

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is \(M,\) radius of its top, \(R\) and height, \(H\), then its moment of inertia about its axis is

A monochromatic beam of light has a frequency \(v = \frac{3}{{2\pi }} \times {10^{12}}\,Hz\) and is propagating along the direction \(\frac{{\hat i + \hat j}}{{\sqrt 2 }}\). It is polarized along the \(\hat k\) direction. The acceptable form for the magnetic field is

The region between two concentric spheres ofradii '\(a\)' and '\(b\)', respectively (see figure), have volume charge density \(\rho = \frac{A}{r}\) where \(A\) is a constant and \(r\) is the distance from the centre. At the centre of the spheres is a point charge \(Q\). The value of \(A\) such that the electric field in the region between the spheres will be constant, is :

The energy required to take a satellite to a height \(‘h’\) above Earth surface (radius of Earth \(= 6.4 \times 10^3\,km\) ) is \(E_1\) and kinetic energy required for the satellite to be in a circular orbit at this height is \(E_2.\) The value of \(h\) for which \(E_1\) and \(E_2\) are equal is

A plane progressive wave is given by \(y=2 \cos 2 \pi(330 t-x) m\). The frequency of the wave is _______.

A conductor lies along the \(z-\)axis \(a\) \(-1.5\)\( \le Z < 1.5\,m\) carries a fixed current of \(10.0\ A\) in \( - {\hat a_z}\) direction (see figure). For a field \(\vec B\) \(=\) \(3.0 \times  10^{-4}\)  \(e^{-0.2x}\) \({\hat a_y}\,T\) find the power required to move the conductor at constant speed to \(x = 2.0\ m, y = 0\ m\) in \(5 \times 10^{-3}\ s\). Assume parallel motion along the \(x-\)axis........\( W\)

Unpolarized light of intensity \(I\) is incident on a system of two polarizers, \(A\) followed by \(B.\)  The intensity of emergent light is \(I/2.\)  If a third polarizer \(C\)  is placed between \(A\) and \(B,\)  the intensity of emergent light is reduced to \(I/3 .\)  The angle between the polarizers \(A\) and \(C\) is \(\theta \) . Then