When UV light of wavelength \(300 \mathrm{~nm}\) is incident on the metal surface having work function \(2.13 \mathrm{eV}\), electron emission takes place. The stopping potential is _______. (Given hc \(=1240 \mathrm{eV} \mathrm{nm}\) )

An \(LCR\) circuit contains resistance of \(110 \, \Omega\) and a supply of \(220\, V\) at \(300 \,rad / s\) angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by \(45^{\circ}\). If on the other hand, only inductor is removed the current leads by \(45^{\circ}\) with the applied voltage. The rms current flowing in the circuit will be ...... \(A\)

A thin disc of radius \(b = 2a\)  has a concentric hole of radius \('a'\) in it (see figure). It carries uniform surface charge \('\sigma '\) on it. If the electric field on its axis at height \('h'\) \((h << a)\) from its centre is given as \('Ch'\) then value of \('C'\) is

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, \(27\,^oC\).The work done on the gas will be

Given a thin convex lens (refractive index \(\mu_2\) ), kept in a liquid (refractive index \(\mu_1, \mu_1 \lt \mu_2\) ) having radii of curvatures \(\left|R_1\right|\) and \(\left|R_2\right|\). Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

A uniform thin rod \(AB\) of length \(L\) has linear mass density \(\mu \left( x \right) = a + \frac{{bx}}{L}\) , where \(x\) is measured from \(A\). If the \(CM\) of the rod lies at a distance of \(\left( {\frac{7}{12}} \right)L\) from \(A\), then \(a\) and \(b\) are related as

A simple pendulum made of a bob of mass \(m\) and a metallic wire of negligible mass has time period \(2s\) at  \(T = 0\,^oC\) . If the temeprature of the wire is increased and the corresponding change in its time peirod is plotted against its temperature, the resulting graph is a line of slope \(S\). If the coefficient of linear expansion of metal is \(\alpha \) then the value of  \(S\) is

A machine gun of mass \(10\,kg\) fires \(20\,g\) bullets at the rate of \(180\) bullets per minute with a speed of \(100\,m s ^{-1}\) each. The recoil velocity of the gun is \(.............\,m/s\)

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled \(3\, m\) is ................ \(\mathrm{J}\)

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in\(P-V\) diagram. The relation between the ratio \(\frac{V_a}{V_d}\) and the ratio \(\frac{V_b}{V_c}\) is _______.

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

List\(-I\)	List\(-II\)
\((a)\) Isothermal	\((i)\) Pressure constant
\((b)\) Isochoric	\((ii)\) Temperature constant
\((c)\) Adiabatic	\((iii)\) Volume constant
\((d)\) Isobaric	\((iv)\) Heat content is constant

Choose the correct answer from the options given below

For the given circuit, comment on the type of transformer used:

Consider a Disc of mass \(5 \mathrm{~kg}\), radius \(2 \mathrm{~m}\), rotating with angular velocity of \(10 \mathrm{rad} / \mathrm{s}\) about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is _______ \(J\).