In the following \(p-V\) diagram the equation of state along the curved path is given by \((V-2)^2=4\) ap where \(a\) is a constant. The total work done in the closed path is

An object of mass \(1 kg\) is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be \(....MJ\)[If, \(g =10\,ms ^{-2}\) and radius of earth \(=6400\,km\) ]

A circuit to verify \(Ohm's\) law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \(\frac{C_p}{C_v}\) for the gas is:

The electric field of an electromagnetic wave in free space is \(\overrightarrow{\mathrm{E}}=57 \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](4 \hat{i}-3 \hat{j}) N / C\). The associated magnetic field in Tesla is _______.

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.

The motion of a simple pendulum excuting \(S.H.M\). is represented by following equation. \(Y = A \sin (\pi t +\phi)\), where time is measured in \(second\). The length of pendulum is .............\(cm\)

The position vector of a particle related to time \(t\) is given by \(\overrightarrow{ r }=\left(10 t \hat{ i }+15 t ^2 \hat{ j }+7 \hat{ k }\right) m\) The direction of net force experienced by the particle is

The energy associated with electric field is \((U_E)\) and with magnetic field is \((U_B)\) for an electromagnetic wave in free space. Then

A string \(A\) of length \(0.314\) m and Young's modulus \(2 \times 10^{10}\) N/m\(^2\) is connected to another string \(B\) of length and Young's modulus both twice of those of \(A\). This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass \(0.8\) kg. The net change in length of the combination is _____ mm. (radius of both the strings is \(0.2\) mm and acceleration due to gravity \(= 10\) m/s\(^2\)) (Mass of both strings is to be neglected as compared to the mass of load)

A string is wrapped around the rim of a wheel of moment of inertia \(0.40 \mathrm{kgm}^2\) and radius \(10 \mathrm{~cm}\). The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of \(40 \mathrm{~N}\). The angular velocity of the wheel after \(10\) \(\mathrm{s}\) is \(\mathrm{x} \mathrm{rad} / \mathrm{s}\), where \(\mathrm{x}\) is _______.

In the circuit shown, the potential difference between \(A\) and \(B\) is ............. \(V\)

The logic gate equivalent to the given circuit diagram is: