Force between two point charges \(q_1\) and \(q_2\) placed in vacuum at ' \(r\) ' \(\mathrm{cm}\) apart is \(F\). Force between them when placed in a medium having dielectric \(\mathrm{K}=5\) at ' \(\mathrm{r} / 5\) ' \(\mathrm{cm}\) apart will be _______.

The distance between object and its \(3\) times magnified virtual image as produced by a convex lens is \(20 \mathrm{~cm}\). The focal length of the lens used is _______ \(\mathrm{cm}\).

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

A sphere of capacitance \(100\) pF is charged to a potential of \(100\) V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7}\) J. The value of \(\alpha\) is __________. (combined capacitance of spheres is \(200\) pF)

Due to presence of an em-wave whose electric component is given by \(\mathrm{E}=100 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{NC}^{-1}\), a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

For a uniformly charged ring of radius \(R\), the electric field on its axis has the largest magnitude at a distance \(h\) from its centre. Then value of \(h\) is

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as \(100\) Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by \(30^{\circ}\) in clockwise direction, the intensity of emerging light will be .......... Lumens.

A current of \(200\  \mu \mathrm{A}\) deflects the coil of a moving coil galvanometer through \(60^{\circ}\). The current to cause deflection through \(\frac{\pi}{10}\) radian is:

Eight mercury drops, each of radius \(r\), coalesce to form a bigger drop. The surface energy released in this process is _______. (\(S\) is the surface tension of mercury).

In the circuit shown, current (in \(A\)) through \(50\; V\) and \(30\; V\) batteries are, respectively

An object is taken to a height above the surface of earth at a distance \(\frac{5}{4} R\) from the centre of the earth. Where radius of earth, \(R=6400\,km\). The percentage decrease in the weight of the object will be \(....\%\)