The focal length \(f\) is related to the radius of curvature \(R\) of the spherical convex mirror by

Given below are two statements: Statement\(- I\) : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement\(- II\): Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field. Choose the \(CORRECT\) answer from the options given below : -

In Young's double slit experiment, if the source of light changes from orange to blue then

Two waves are simultaneously passing through a string and their equations are : \({y}_{1}={A}_{1} \sin {k}({x}-v {t}), {y}_{2}={A}_{2} \sin {k}\left({x}-{vt}+{x}_{0}\right) .\) Given amplitudes \({A}_{1}=12\, {mm}\) and \({A}_{2}=5\, {mm}\) \({x}_{0}=3.5\, {cm}\) and wave number \({k}=6.28\, {cm}^{-1}\). The amplitude of resulting wave will be \(......\,{mm}\)

The bob of a simple pendulum has mass \(2\,g\) and a charge of \(5.0\,\mu C\). It is at rest in a uniform horizontal electric field of intensity \(2000\,\frac{V}{m}\). At equilibrium, the angle that the pendulum makes with the vertical is (take \(g = 10\,\frac{m}{{{s^2}}}\))

\(300 \,cal\). of heat is given to a heat engine and it rejects \(225 \,cal\). of heat. If source temperature is \(227^{\circ} C\), then the temperature of sink will be____\({ }^{\circ} C\).

The root mean square speed of smoke particles of mass \(5 \times 10^{-17}\,kg\) in their Brownian motion in air at NTP is approximately \(.......\,mm\,s ^{-1}\) [Given \(k =1.38 \times 10^{-23}\,J\,K ^{-1}\) ]

Particle \(A\) of mass \(m _{1}\) moving with velocity \((\sqrt{3} \hat{i}+\hat{j})\, ms ^{-1}\) collides with another particle \(B\) of mass \(m _{2}\) which is at rest initially. Let \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) be the velocities of particles \(A\) and \(B\) after collision respectively. If \(m _{1}=2\, m _{2}\) and after collision \(\overrightarrow{ V }_{1}=(\hat{ i }+\sqrt{3} \hat{ j })\, ms ^{-1},\) the angle between \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) is\(......^o\)

A copper rod of mass \(m\) slides under gravity on two smooth parallel rails, with separation \(l\) and set at an angle of \(\theta\) with the horizontal. At the bottom, rails are joined by a resistance \(R\). There is a uniform magnetic field \(B\) normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is

The surface charge density of a thin charged disc of radius \(R\) is \(\sigma \). The value of the electric field at the centre of the disc is \(\frac{\sigma }{{2\,{ \in _0}}}\). With respect to the field at the centre, the electric field along the axis at a distance \(R\) from the centre of the disc

A positive charge \('q'\) of mass \('m'\) is moving along the \(+ x\) axis. We wish to apply a uniform magnetic field \(B\) for time \(\Delta t\) so that the charge reverses its direction crossing the \(y\) axis at a distance \(d.\) Then

An \(AC\) current is given by \(I = I _{1} \sin \omega t + I _{2} \cos \omega t\). A hot wire ammeter will give a reading