A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is _______. (Given \(=\) Radius of geo-stationary orbit for earth is \(4.2 \times 10^4 \mathrm{~km}\) )

With reference to the observations in photo-electric effect, identify the correct statements from below: \(A.\) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. \(B.\) The value of saturation current increases on moving the source of light away from the metal surface. \(C.\) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light. \(D.\) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves. \(E.\) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves. Choose the correct answer from the options given below:

A telegraph line of length \(100 \,km\) has a capacity of \(0.01\,\mu F / km\) and it carries an alternating current at \(0.5 \,kilo \,cycle \,per \,second\). If minimum impedance is required, then the value of the inductance that needs to be introduced in series is__________ \(m H\). \(\text { (if } \pi=\sqrt{10})\)

\({T}_{0}\) is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to \(\frac{1}{16}\) times of its initial value, the modified time

In the reported figure, two bodies \(A\) and \(B\) of masses \(200\, {g}\) and \(800\, {g}\) are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be \(.....\,{rad} / {s}\) when \({k}=20 \,{N} / {m} .\)

In a Young’s double slit experiment with slit separation \(0.1\, mm\), one observes a bright fringe at angle \(\frac{1}{{40}}\, rad\) by using light of wavelength \({\lambda _1}\). When the light of wavelength \(\lambda _2\) is used a bright fringe is seen at the same angle in the same set up. Given that \({\lambda _1}\) and \({\lambda _2}\) are in visible range (\(380\, nm\) to \(740\, nm\)), their values are

Unpolarised light of intensity \(32\,Wm ^{-2}\) passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is \(3\,Wm ^{-2}\), then the angle between pass axis of first two polaroids is \(............\,^{\circ}\)

A thermally insulted vessel contains \(150\, g\) of water at \(0\,^oC\). Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at \(0\,^oC\) itself. The mass of evaporated water will be closes to ....... \(g\) (Latent heat of vaporization of water \(= 2.10 \times10^6\, Jkg^{-1}\) and Laten heat of Fusion of water \( = 3.36 \times10^5\,Jkg^{-1}\) )

In finding out refractive index of glass slab the following observations were made through travelling microscope \(50\) vernier scale division \(=\) \(49 \mathrm{MSD} ; 20\) divisions on main scale in each \(\mathrm{cm}\) For mark on paper \(\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26\) For mark on paper seen through slab \(\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41\) For powder particle on the top surface of the glass slab \(\mathrm{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1\) \((\mathrm{MSR}=\) Main Scale Reading, \(\mathrm{VC}=\) Vernier Coincidence) Refractive index of the glass slab is _______.

A train is moving on a straight track with speed \(20\ ms^{-1}\). It is blowing its whistle at the frequency of \(1000\ Hz\). The percentage change in the frequency heard by a person standing near the track as the train passes him is ( speed of sound \(=320\) \(ms^{-1}\) ) close to .... \(\%\)

With increasing biasing voltage of a photodiode, the photocurrent magnitude