A bus moving along a straight highway with speed of \(72 \mathrm{~km} / \mathrm{h}\) is brought to halt within \(4 \mathrm{~s}\) after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is __________\(\mathrm{m}\).

When radiation of wavelength \(\lambda \) is incident on a metallic surface, the stopping potential is \(4.8\) volts. If the same surface is illuminated with radiation of double the wavelength, then the stopping potential becomes \(1.6\) volts. Then the threshold wavelength for the surface is

Magnitude of magnetic field (in \(SI\) units) at the centre of a hexagonal shape coil of side \(10\, cm\), \(50\) turns and carrying current \(I\) (Ampere) in units of \(\frac{\mu_{0} I}{\pi}\) is

Space between two concentric conducting spheres of radii \(a\) and \(b (b > a)\) is filled with \(a\) medium of resistivity \(\rho \). The resistance between the two spheres will be

A piece of bone of an animal from a ruin is found to have \(^{14}C\) activity of \(12\) disintegrations per minute per gm of its carbon content. The \(^{14}C\) activity of a living animal is \(16\) disintegrations per minute per gm. How long ago nearly did the animal die? ............\(years\) (Given halflife of \(^{14}C\) is \(t_{1/2} = 5760\,years\) )

A thin rod of mass \(0.9\, kg\) and length \(1 \,m\) is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move \(0.1\, kg\) moving in a straight line with velocity \(80\,m / s\) hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in \(rad/s\)) of the rod immediately after the collision will be

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and \(2 \sqrt{3}\) (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is _________ .

The total charge enclosed in an incremental volume of \(2 \times 10^{-9} \,{m}^{3}\) located at the origin is ...... \(nC,\) if electric flux density of its field is found as \(D=e^{-x} \sin y \hat{i}-e^{-x} \cos y \hat{j}+2 z \hat{k}\, C / m^{2}\)

\(5\) moles of unknown gas is heated at constant volume from \(10 \, °C\) to \(20 \, °C\). The molar specific heat of this gas at constant pressure \(c_p = 8\) cal/mol.°C and \(R = 8.36\) J/mol.°C. The change in the internal energy of the gas is _______ calorie.