A metallic rod of length ' \(L\) ' is rotated with an angular speed of ' \(\omega\) ' normal to a uniform magnetic field ' \(B\) ' about an axis passing through one end of rod as shown in figure. The induced emf will be :

The angular frequency of alternating current in a \(L-C-R\) circuit is \(100\, rad / s\). The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Two point charges \(q_1=3\,\mu C\) and \(q_2=-4\,\mu C\) are placed at points \((2\hat{i}+3\hat{j}+3\hat{k})\) and \((\hat{i}+\hat{j}+\hat{k})\) respectively. Force on charge \(q_2\) is ________ N. \(\left(\text{Take } \dfrac{1}{4\pi\epsilon_0} = 9\times 10^9 \text{ SI Units}\right)\)

Select the correct statement from the following

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is ................

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa).

A shown in the figure, a battery of \(emf \;\varepsilon\) is connected to an inductor \(L\) and resistance \(R\) in series. The switch is closed at \(t=0 .\) The total charge that flows from the battery, between \(\mathrm{t}=0\) and \(\mathrm{t}=\mathrm{t}_{\mathrm{c}}\;( \mathrm{t}_{\mathrm{c}}\) is the time constant of the circuit) is

Match List \(I\) with List \(II\)

List \(I\)	List \(II\)
\(A\) Spring constant	\(I\) \((T ^{-1})\)
\(B\) Angular speed	\(II\) \((MT ^{-2})\)
\(C\) Angular momentum	\(III\) \((ML ^2)\)
\(D\) Moment of Inertia	\(IV\) \((ML ^2 T ^{-1})\)

Choose the correct answer from the options given below

An elevator in a building can carry a maximum of \(10\) persons, with the average mass of each person being \(68\; kg\). The mass of the elevator itself is \(920\; kg\) and it moves with a constant speed \(3\; \mathrm{m} / \mathrm{s}\). The frictional force opposing the motion is \(6000 \;\mathrm{N}\). If the elevator is moving up with its full capacity, the 10.Power delivered by the motor to the elevator \(\left(\mathrm{g}=10 \;\mathrm{m} / \mathrm{s}^{2}\right)\) must be at least .............. \(\mathrm{W}\)

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V , what is the wavelength of the em-wave ?
(Given hc \(=1242 \mathrm{eVnm}\) where h is the Planck's constant and c is the speed of light in vaccum.)