Surface of certain metal is first illuminated with light of wavelength \({\lambda _1} = 350\,nm\) and then, the light of wavelength \({\lambda _2} = 540\,nm\). It is found that the maximum speed of the photo electrons in the two cases differ by a factor of \(2\). The work function of the metal (in \(eV\)) is close to: (Energy of photon \( = \frac{{1240}}{{\lambda {\rm{(in\, nm)}}}}\,eV\))

A raindrop with radius \(R=0.2\, {mm}\) fells from a cloud at a height \(h=2000\, {m}\) above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attainde by the raindrop is : (In \({ms}^{-1}\)) [Density of water \(f_{{w}}=1000\;{kg} {m}^{-3}\) and density of air \(f_{{a}}=1.2\; {kg} {m}^{-3}, {g}=10 \;{m} / {s}^{2}\) Coefficient of viscosity of air \(=18 \times 10^{-5} \;{Nsm}^{-2}\) ]

A parallel plate capacitor of area \(A=16 \mathrm{~cm}^2\) and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area \(\mathrm{A}_0=3.2 \mathrm{~cm}^2\) inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through \(\mathrm{A}_0\) is ________ mA .

A slender uniform rod of mass \(M\) and length \(l\) is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle \(\theta\) with the vertical is

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is \({W}\), then weight of the same object on that planet will be

Two identical springs of spring constant \('2k'\) are attached to a block of mass \(m\) and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this sytem is ...... .

Two projectile thrown at \(30^{\circ}\) and \(45^{\circ}\) with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

The centre of mass of a solid hemisphere of radius \(8\, cm\) is \(X \,cm\) from the centre of the flat surface. Then value of \(x\) is\(......\)

On the \(x-\)axis and a dsitance \(x\) from the origin, the gravitational field due to a mass distribution is given by \(\frac{A x}{\left(x^{2}+a^{2}\right)^{3 / 2}}\) in the \(x-\)direction. The magnitude of gravitational potential on the \(x-\)axis at a distance \(x,\) taking its value to be zero at infinity, is

The pressure wave, \(P = 0.01\,sin\,[1000t -3x]\,Nm^{-2},\) corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is \(0\,^oC.\) On some other day when temperature is \(T,\) the speed of sound produced by the same blade and at the same frequency is found to be \(336 \,ms^{-1}\). Approximate value of \(T\) is .... \(^oC\)

A force of \(10 \; N\) acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be ...... \(N\)

Time period of a simple pendulum is \(T\). The time taken to complete \(5 / 8\) oscillations starting from mean position is \(\frac{\alpha}{\beta} T\). The value of \(\alpha\) is ..... .