Electric field in a plane electromagnetic wave is given by \({E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}\) The velocity of electromagnetic wave in this medium is : (Given \({C}=\) speed of light in vacuum)

The exit surface of a prism with refractive index \(n\) is coated with a material having refractive index \(\frac{ n }{2}\). When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is _________

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.

A beam of electromagnetic radiation of intensity \(6.4 \times 10^{-5}\; \mathrm{W} / \mathrm{cm}^{2}\) is comprised of wavelength, \(\lambda=310 \;\mathrm{nm} .\) It falls normally on a metal (work function \(\varphi=2 \;\mathrm{eV}\) ) of surface area of \(1\; \mathrm{cm}^{2} .\) If one in \(10^{3}\) photons ejects an electron, total number of electrons ejected in \(1 \;s\) is \(10^{\mathrm{x}}\).then \(\mathrm{x}\) is \(\left(\mathrm{hc}=1240\; \mathrm{eV} \mathrm{nm}, 1\; \mathrm{eV}=1.6 \times 10^{-19} \;\mathrm{J}\right)\)

An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume \(\mathrm{M}=\) mass of earth, \(\mathrm{G}=\) Universal gravitational constant)

\(C_1\) and \(C_2\) are two hollow concentric cubes enclosing charges \(2 Q\) and \(3 Q\) respectively as shown in figure. The ratio of electric flux passing through \(C_1\) and \(C_2\) is _______.

A galvanometer having a coil of resistance \(30 \Omega\) need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be \(\frac{30}{X} \Omega\), where \(X\) is ________.

In \(5\, minutes,\) a body cools from \(75^{\circ} {C}\) to \(65^{\circ} {C}\) at room temperature of \(25^{\circ} {C}\). The temperature of body at the end of next \(5\, minutes\) is \(......\,{ }^{\circ} {C} .\)

A uniform solid cylinder of mass ' \(m\) ' and radius ' \(r\) ' rolls along an inclined rough plane of inclination \(45^{\circ}\). If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be