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 plane is in level flight at constant speed and each of its two wings has an area of \(40 \mathrm{~m}^2\). If the speed of the air is \(180 \mathrm{~km} / \mathrm{h}\) over the lower wing surface and \(252 \mathrm{~km} / \mathrm{h}\) over the upper wing surface, the mass of the plane is _______ \(\mathrm{kg}\). (Take air density to be \(1 \mathrm{~kg} \mathrm{~m}^{-3}\) and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

A cricket player catches a ball of mass \(120 \mathrm{~g}\) moving with \(25 \mathrm{~m} / \mathrm{s}\) speed. If the catching process is completed in \(0.1 \mathrm{~s}\) then the magnitude of force exerted by the ball on the hand of player will be _______ (in SI unit).

Two cars \(P\) and \(Q\) are moving on a road in the same direction. Acceleration of car \(P\) increases linearly with time whereas car \(Q\) moves with a constant acceleration. Both cars cross each other at time \(t=0\), for the first time. The maximum possible number of crossing(s) (including the crossing at \(t=0)\) is ________.

A particle of mass \(100\,g\) is projected at time \(t =0\) with a speed \(20\,ms ^{-1}\) at an angle \(45^{\circ}\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(t=2\,s\) is found to be \(\sqrt{ K }\,kg\,m ^2 / s\). The value of \(K\) is \(............\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]

At what temperature (in \( ^{\circ} C\)) a gold ring of diameter \(6.230\) \(cm\) be heated so that it can be fitted on a wooden bangle of diameter \(6.241 \,cm\) ? Both the diameters have been measured at room temperature \(\left(27^{\circ} C \right)\). (Given: coefficient of linear thermal expansion of gold \(\alpha_{L}=1.4 \times 10^{-5} \,K ^{-1}\) )

In a coil, the current changes form \(-2 \mathrm{~A}\) to \(+2 \mathrm{~A}\) in \(0.2 \mathrm{~s}\) and induces an emf of \(0.1 \mathrm{~V}\). The selfinductance of the coil is _______.

The velocity of a small ball of mass ' \(m\) ' and density \(d _{1}\), when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is \(d _{2}\), then the viscous force acting on the ball, will be

In the electric network shown, when no current flows through the \(4\, \Omega \) resistor in the arm \(EB\), the potential difference between the points \(A\) and \(D\) will be ............... \(V\)

The \(Q\)-value of a nuclear reaction and kinetic energy of the projectile particle, \(K _{ p }\) are related as