In series \(LCR\) circuit, the capacitance is changed from \(\mathrm{C}\) to \(4 \mathrm{C}\). To keep the resonance frequency unchanged, the new inductance should be _______.

Three identical resistors with resistance \(R=12 \Omega\) and two identical inductors with sell inductance \(L=5 mH\) are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _________ A.

Two coaxial discs, having moments of inertia \(I_1\) and \(\frac{I_1}{2}\) are a rotating with respectively angular velocities \(\omega_1\) and \(\frac{\omega_1}{2}\), about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f -E_i)\) is

An unknown metal of mass \(192\, g\) heated to a temperature of \(100\,^oC\) was immersed into a brass calorimeter of mass \(128\, g\) containing \(240\, g\) of water at a temperature of \(8.4\,^oC\). Calculate the specific heat of the unknown metal if water temperature stabilizes at \(21.5\,^oC\). (Specific heat of brass is \(394\, J\, kg^{-1}\, K^{-1}\)) ......... \(J\, kg^{-1}\, K^{-1}\)

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density \(\sigma_{\mathrm{o}}\). Choose the correct option from the following.

A man in a car at location \(Q\) on a straight highway is moving with speed \(v\). He decides to reach a point \(P\) in a field at a distance \(d\) from highway (point \(M\) ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance \(RM\), so that the time taken to reach \(P\) is minimum?

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

A clock has \(75 \mathrm{~cm}, 60 \mathrm{~cm}\) long second hand and minute hand respectively. In \(30\) minutes duration the tip of second hand will travel \(x\) distance more than the tip of minute hand. The value of \(x\) in meter is nearly _______. (Take \(\pi=3.14\) )