A conducting circular loop is placed in \(X - Y\) plane in presence of magnetic field \(\overrightarrow{ B }=\left(3 t ^{3} \hat{ j }+3 t ^{2} \hat{ k }\right)\) in SI unit. If the radius of the loop is \(1 m\), the induced emf in the loop, at time, \(t =2\,s\) is \(n \pi V\). The value of \(n\) is.

According to kinetic theory of gases, \(A\). The motion of the gas molecules freezes at \(0^{\circ} C\) \(B\). The mean free path of gas molecules decreases if the density of molecules is increased. \(C\). The mean free path of gas molecules increases if temperature is increased keeping pressure constant. \(D\). Average kinetic energy per molecule per degree of freedom is \(\frac{3}{2} k_{B} T\) (for monoatomic gases) Choose the most appropriate answer from the options given below

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

A coin is placed on a disc. The coefficient of friction between the coin and the disc is \(\mu\). If the distance of the coin from the center of the disc is \(r\), the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is _______.

A force of \(40\, N\) acts on a point \(B\) at the end of an \(L-\) shaped object, as shown in the figure. The angle \(\theta\) that will produce maximum moment of the force about point \(A\) is given by

Two uniformly charged spherical conductors \(A\) and \(B\) of radii \(5 mm\) and \(10 mm\) are separated by a distance of \(2 cm\). If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere \(A\) and \(B\) will be .

Starting with the same initial conditions, an ideal gas expands from volume \(V_{1}\) to \(V_{2}\) in three different ways. The work done by the gas is \(W_{1}\) if the process is purely isothermal. \(W _{2}\). if the process is purely adiabatic and \(W _{3}\) if the process is purely isobaric. Then, choose the coned option

An electron is travelling with a velocity \(v\) in free space and when it enters a medium, its velocity is reduced by \(20\%\). The de Broglie wavelength of electron in the medium is \(\alpha\lambda_0\), where \(\lambda_0\) is its de Broglie wavelength in free space. The value of \(\alpha\) is _______.

A very long (length \(L\) ) cylindrical galaxy is made of uniformly distributed mass and has radius \(R(R < < L).\) A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is \(T\) and its distance from the galaxy's axis is \(r,\) then

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes \(32\) times of its initial value. If the final pressure of gas is \(128\) atmosphers, the value of \(\gamma\) the gas is

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is

A resonance circuit having inductance and resistance \(2 \times 10^{-4} H\) and \(6.28 \Omega\) respectively oscillates at \(10\, MHz\) frequency. The value of quality factor of this resonator is ......... \([\pi=3.14]\)