Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of \(\theta ,\) where \(\theta \) is the angle by which it has rotated, is given as \(k\theta ^2.\) If its moment of inertia is \(I\) then the angular acceleration of the disc is

One mole of a diatomic ideal gas undergoes a cyclic process \(ABC\) as shown in figure. The process \(BC\) is adiabatic. The temperatures at \(A, B\) and \(C\) are \(400\ K, 800\ K \) and \(600\ K\) respectively. Choose the correct statement

A positive ion \(A\) and a negative ion \(B\) has charges \(6.67 \times 10^{-19} \mathrm{C}\) and \(9.6 \times 10^{-10} \mathrm{C}\), and masses \(19.2 \times 10^{-27} \mathrm{~kg}\) and \(9 \times 10^{-27} \mathrm{~kg}\) respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is \(P \times 10^{45}\), where the value of 10\(P\) is _______.
(Take \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1}\) and universal gravitational constant as \(6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}\) )
Assume that charge may not be an integral multiple of electrons.

When a ball is dropped into a lake from a height \(4.9 \,m\) above the water level, it hits the water with a velocity \(v\) and then sinks to the bottom with the constant velocity \(v\). It reaches the bottom of the lake \(4.0,s\) after it is dropped. The approximate depth of the lake is ............ \(m\)

A light rope is wound around a hollow cylinder of mass \(5\,kg\) and radius \(70\,cm\). The rope is pulled with a force of \(52.5\,N\). The angular acceleration of the cylinder will be.....\( {rad \,s}{ }^{-2}\).

For a series \(LCR\) circuit with \({R}=100\,\ \Omega, {L}=0.5\, {mH}\) and \({C}=0.1\, {pF}\) connected across \(220 \,{V}-50\, {Hz}\) \(AC\) supply, the phase angle between current and supplied voltage and the nature of the circuit is :

The diameter of a spherical bob is measured using a vernier callipers. \(9\) divisions of the main scale, in the vernier callipers, are equal to \(10\) divisions of vernier scale. One main scale division is \(1\, {mm}\). The main scale reading is \(10\, {mm}\) and \(8^{\text {th }}\) division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of \(0.04\, {cm}\), then the radius of the bob is \(...... \,\times 10^{-2} \,{cm}\)

A gas has \(n\) degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be.

The magnitude of torque on a particle of mass \(1\,kg\) is \(2.5\, Nm\) about the origin. If the force acting on it is \(1\,N\), and the distance of the particle from the origin is \(5\,m\), the angle between the force and the position vector is (in radians)

A plane electromagnetic wave of frequency \(20\,MHz\) propagates in free space along \(x\)-direction. At a particular space and time, \(\overrightarrow{ E }=6.6 \hat{ j } V / m\). What is \(\overrightarrow{ B }\) at this point?

The sum of two forces \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) is \(\overrightarrow{\mathrm{R}}\) such that \(|\overrightarrow{\mathrm{R}}|=|\overrightarrow{\mathrm{P}}| .\) The angle \(\theta\) (in degrees) that the resultant of \(2 \overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) will make with \(\overrightarrow{\mathrm{Q}}\) is