A uniform sphere of mass \(500\; g\) rolls without slipping on a plane horizontal surface with its centre moving at a speed of \(5.00\; \mathrm{cm} / \mathrm{s}\). Its kinetic energy is

In a Young’s double slit experiment, the slits are placed \(0.320\,mm\) apart. Light of wavelength \(\lambda = 500\,nm\) is incident on the slits. The total number of bright fringes that are observed in the angular range \( - {30^o} \le \theta  \le {30^o}\) is

Identify the pair of physical quantities that have same dimensions

The frequency of echo will be \(.......Hz\) if the train blowing a whistle of frequency \(320\,Hz\) is moving with a velocity of \(36\,km / h\) towards a hill from which an echo is heard by the train driver. Velocity of sound in air is \(330\,m / s\).

A thin prism with angle \( 5^{\circ} \) of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is ___________.

The specific heat at constant pressure of a real gas obeying \(\mathrm{PV}^2=\mathrm{RT}\) equation is _______.

A coaxial cable consists of an inner wire of radius \('a'\) surrounded by an outer shell of inner and outer radii ' \({b}\) ' and '\(c\)' respectively. The inner wire carries an electric current is, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance \({x}\) from the axis when \((i)\) \({x}<{a}\) and \((ii)\) \({a}<{x}<{b}\) ?

A bimetallic strip consists of metals \(A\) and \(B\). It is mounted rigidly as shown. The metal \(A\) has higher coefficient of expansion compared to that of metal \(B\). When the bimetallic strip is placed in a cold both, it will :

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

The radius of curvature of each surface of a convex lens having refractive index \(1.8\) is \(20\,cm\). The lens is now immersed in a liquid of refractive index \(1.5\). The ratio of power of lens in air to its power in the liquid will be \(x : 1\). The value of \(x\) is \(.....\)

An electric charge \(10^{-6} \mu \mathrm{C}\) is placed at origin \((0,0)\) \(\mathrm{m}\) of \(\mathrm{X}-\mathrm{Y}\) co-ordinate system. Two points \(\mathrm{P}\) and \(\mathrm{Q}\) are situated at \((\sqrt{3}, \sqrt{3}) \mathrm{m}\) and \((\sqrt{6}, 0) \mathrm{m}\) respectively. The potential difference between the points \(P\) and \(Q\) will be :