A lift of mass \(M =500\,kg\) is descending with speed of \(2\,ms ^{-1}\). Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of \(2\,ms ^{-2}\). The kinetic energy of the lift at the end of fall through to a distance of \(6 m\) will be \(...........kJ.\)

A uniform rod of mass m and length \(l\) suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _________.(g acceleration due to gravity)

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object ' O ' is :
( C is the center of curvature of the spherical surface and \(R\) is the radius of curvature)

In young's double slit experiment performed using a monochromatic light of wavelength \(\lambda\), when a glass plate \((\mu=1.5)\) of thickness \(x \lambda\) is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of \(x\) will be..........

A point charge +q is placed at the origin. A second point charge +9 q is placed at \((\mathrm{d}, 0,0)\) in Cartesian coordinate system. The point in between them where the electric field vanishes is :

A rod of length 5 L is bent right angle keeping one side length as 2 L.

The position of the centre of mass of the system: (Consider \(\mathrm{L}=10 \mathrm{~cm}\))

A ray of light passing through a prism \((\mu=\sqrt{3})\) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ..... . (in degrees)

When a dc voltage of \(100 \mathrm{~V}\) is applied to an inductor, a dc current of \(5 \mathrm{~A}\) flows through \(1\) . When an ac voltage of \(200 \mathrm{~V}\) peak value is connected to inductor, its inductive reactance is found to be \(20 \sqrt{3} \Omega\). The power dissipated in the circuit is _______\(W\).

A parallel plate capacitor of capacitance \(12.5 \mathrm{pF}\) is charged by a battery connected between its plates to potential difference of \(12.0 \mathrm{~V}\). The battery is now disconnected and a dielectric slab \(\left(\epsilon_{\mathrm{r}}=6\right)\) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _______.\(\times 10^{-12} \mathrm{~J}\).

Two ions of masses \(4 \,{amu}\) and \(16\, amu\) have charges \(+2 {e}\) and \(+3 {e}\) respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

In an expression a \(\times 10^{\mathrm{b}}\) _______.

A capacitor has air as dielectric medium and two conducting plates of area \(12 \mathrm{~cm}^2\) and they are \(0.6 \mathrm{~cm}\) apart. When a slab of dielectric having area \(12 \mathrm{~cm}^2\) and \(0.6 \mathrm{~cm}\) thickness is inserted between the plates, one of the conducting plates has to be moved by \(0.2 \mathrm{~cm}\) to keep the capacitance same as in previous case. The dielectric constant of the slab is _______. (Given \(\left.\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\)

In a photoelectric experiment ultraviolet light of wavelength \(280\, {nm}\) is used with lithium cathode having work function \(\phi=2.5\, {eV}\). If the wavelength of incident light is switched to \(400\, {nm}\), find out the change in the stopping potential (in \({V}\)). \(\left({h}=6.63 \times 10^{-34}\, {J} \cdots\right.\), \(\left.{c}=3 \times 10^{8} \,{ms}^{-1}\right)\)