The light of two different frequencies whose photons have energies \(3.8 \,eV\) and \(1.4 \,eV\) respectively, illuminate a metallic surface whose work function is \(0.6 \,eV\) successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectivly will be

A block is fastened to a horizontal spring. The block is pulled to a distance \(x =10\,cm\) from its equilibrium position (at \(x =0\) ) on a frictionless surface from rest. The energy of the block at \(x =5\) \(cm\) is \(0.25\,J\). The spring constant of the spring is \(.........Nm ^{-1}\)

A beam of plane polarised light of large cross sectional area and uniform intensity of \(3.3 \,Wm ^{-2}\) falls normally on a polariser (cross sectional area \(3 \times 10^{-4}\, m ^{2}\) ) which rotates about its axis with an angular speed of \(31.4\, rad/s.\) The energy of light passing through the polariser per revolution, is close to ........ \( \times 10^{-4} \,J\)

A Spherical ball of radius \(1 mm\) and density \(10.5 g / cc\) is dropped in glycerine of coefficient of viscosity \(9.8\) poise and density \(1.5 g / cc\). Viscous force on the ball when it attains constant velocity is \(3696 \times 10^{-x} N\). The value of \(x\) is \(\text { (Given, } g =9.8 m / s ^2 \text { and } \pi=\frac{22}{7} \text { ) }\)

The weight of a body on the surface of the earth is \(100\,N\). The gravitational force on it when taken at a height, from the surface of earth, equal to onefourth the radius of the earth is \(..........\,N\)

A uniform wire of length \(l\) and radius \(r\) has a resistance of \(100\, \Omega \). It is recast into a wire of radius \(\frac{r}{2}\). The resistance of new wire will be ............... \(\Omega\)

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is \(11.2 \mathrm{~km} / \mathrm{s}\), the escape velocity in \(\mathrm{km} / \mathrm{s}\) from the planet will be :

A circular disc \(D_1\) of mass \(M\) and radius \(R\) has two identical discs \(D_2\) and \(D_3\) of the same mass \(M\) and radius \(R\) attached rigidly as its opposite ends (see figure). The moment of inertia of the system about the axis \(OO\)’, passing through the centre of \(D_1\) as shown in the figure, will

Two infinite planes each with uniform surface charge density \(+\sigma\) are kept in such a way that the angle between them is \(30^{\circ} .\) The electric field in the region shown between them is given by

When unpolarized light is incident at an angle of \(60^{\circ}\) on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is _______.

A prism of refractive index \(\mu\) and angle \(A\) is placed in the minimum deviation position. If the angle of minimum deviation is \(A,\) then the value of \(A\) in terms of \(\mu\) is