A particle is moving in a circular path of radius a under the action of an attractive potential \(U = - \frac{k}{{2{r^2}}}\) Its total energy is

A lamp emits monochromatic green light uniformly in all directions. The lamp is \(3\%\) efficient in converting electrical power to electromagnetic waves and consumes \(100\,W\) of power . The amplitude of the electric field associated with the electromagnetic radiation at a distance of \(5\,m\) from the lamp will be nearly.......\(V/m\)

In photo electric effect \(A.\) The photocurrent is proportional to the intensity of the incident radiation. \(B.\) Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light. \(C.\) Max. \(K.E\) with which photoelectrons are emitted depends on the frequency of incident light. \(D.\) The emission of photoelectrons require a minimum threshold intensity of incident radiation. \(E.\) Max. K.E of the photoelectrons is independent of the frequency of the incident light. Choose the correct answer from the options given below:

In \(1^{\text {st }}\) case, Carnot engine operates between temperatures \(300\,K\) and \(100\,K\). In \(2^{\text {nd }}\) case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in \(2^{\text {ad }}\) case) will be.

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction)

Two \(4\) bits binary numbers, \(A = 1101\) and \(B = 1010\) are given in the inputs of a logic circuit shown in figure below. The output \((Y)\) will be:

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same \(P, V, T\). Heating is started from left side until pressure changes to \(\dfrac{27P}{8}\). If initial volume of each compartment was \(9\) litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas \(C_P/C_V = 1.5\))

Three charges \(Q, +q\) and \(+q\) are placed at the vertices of a right -angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of \(Q\) 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).

An electron of mass \(\mathrm{m}\) and magnitude of charge \(|e|\) initially at rest gets accelerated by a constant electric field \(\mathrm{E}\). The rate of change of de-Broglie wavelength of this electron at time \(t\) ignoring relativistic effects is 

Two cells of same emf but different internal resistances \(I_{1}\) and \(I_{2}\) are connected in series with a resistance \(R\). The value of resistance \(R\), for which the potential difference across second cell is zero, is

A sphere of mass \(2\,kg\) and radius \(0.5\, m\) is rolling with an initial speed of \(1 \,ms ^{-1}\) goes up an inclined plane which makes an angle of \(30^{\circ}\) with the horizontal plane, without slipping. How low will the sphere take to return to the starting point \(A\) ? (in \(second\))