A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field \( \vec{E} \) is applied, the final tension in the string changes.The final tension in the string, when pendulum attains an equilibrium position is __________ .
(g: acceleration due to gravity)

Given below are two statement  Statement \(-I\) : What \(\mu\) amount of an ideal gas undergoes adiabatic change from state \(\left( P _{1}, V _{1}, T _{1}\right)\) to state \(\left( P _{2}, V _{2}, T _{2}\right)\), the work done is \(W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}\), where \(\gamma=\frac{ C _{ P }}{ C _{ V }}\) and \(R =\) universal gas constant, Statement \(-II\) : In the above case. when work is done on the gas. the temperature of the gas would rise. Choose the correct answer from the options given below

For the given cyclic process \(CAB\) as shown for a gas, the work done is ..... \(J\)

Water boils in an electric kettle in \(20\) minutes after being switched on. Using the same main supply, the length of the heating element should be _______ to _______ times of its initial length if the water is to be boiled in \(15\) minutes.

A sample of gas with \(\gamma=1.5\) is taken through an adiabatic process in which the volume is compressed from \(1200\, {cm}^{3}\) to \(300\, {cm}^{3}\). If the initial pressure is \(200\, {kPa}\). The absolute value of the workdone by the gas in the process \(= \,..... J.\)

The maximum and minimum distances of a comet from the Sun are \(1.6 \times 10^{12}\, m\) and \(8.0 \times 10^{10}\, m\) respectively. If the speed of the comet at the nearest point is \(6 \times 10^{4}\, ms ^{-1},\) the speed at the farthest point is ......... \(\times 10^{3}\, m / s\)

The dimension of \(\sqrt{\frac{\mu_0}{\epsilon_0}}\) is equal to that of :
( \(\mu_0=\) Vacuum permeability and \(\epsilon_0=\) Vacuum permittivity)

A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants \(K_1, K_2, K_3, K_4\) arranged as shown in the figure. The effective dielectric constant \(K\) will be

The current sensitivity of a galvanometer can be increased by: \((A)\) decreasing the number of turns \((B)\) increasing the magnetic field \((C)\) decreasing the area of the coil \((D)\) decreasing the torsional constant of the spring Choose the most appropriate answer from the options given below.

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?

A solenoid having area \(A\) and length ' \(l\) ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :