A capacitor with capacitance \(5\,\mu F\) is charged to \(5\,\mu C.\) If the plates are pulled apart to reduce the capacitance to \(2\,\mu F,\) how much work is done?

The initial velocity \(v_{i}\) required to project a body vertically upward from the surface of the earth to reach a height of \(10\, R ,\) where \(R\) is the radius of the earth, may be described in terms of escape velocity \(v_{ e }\) such that \(v_{i}=\sqrt{\frac{x}{y}} \times v_{ e } .\) The value of \(x\) will be ...... .

A Young's doublc\(-\)slit experiment is performed using monochromatic light of wavelength \(\lambda\). The intensity of light at a point on the screen, where the path difference is \(\lambda,\) is \(K\) units. The intensity of light at a point where the path difference is A \(\frac{\lambda}{6}\) is given by \(\frac{n K}{12},\) where \(n\) is an integer. The value of \(n\) is\(......\)

A cord is wound round the circumference of wheel of radius \(r\). The axis of the wheel is horizontal and the moment of inertia about it is \(I. \,A\) weight \(mg\) is attached to the cord at the end. The weight falls from rest. After falling through a distance \( 'h '\), the square of angular velocity of wheel will be ..... .

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths \(\lambda _N,\,\lambda _A\)  respectively. The ratio \(\frac{{{\lambda _N}}}{{{\lambda _A}}}\)  is closest to

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is :

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is \(16\). The intensity of the waves are in the ratio

A coil of \(200\) turns and area \(0.20 \mathrm{~m}^2\) is rotated at half a revolution per second and is placed in uniform magnetic field of \(0.01 \mathrm{~T}\) perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is \(\frac{2 \pi}{\beta}\) volt. The value of \(\beta\) is _______.

In the Bohr model an electron moves in a circular orbit around the proton . Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom; when the electron is in \(n^{th}\) excited state, is