Photoelectric emission is observed from a metallic surface for frequencies \(v_1\) and \(v_2\) of the incident light \(\left(v_1>v_2\right)\). If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio \(1: n\), then the threshold frequency of the metallic surface is

A circular disc of radius \(R\) and thickness \(\frac{R}{6}\) has moment of inertia \(I\) about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

A common emitter transistor amplifier has a current gain of 50 . If the load resistance is \(4 \mathrm{k} \Omega\) and input resistance is \(500 \Omega\), the voltage gain of the amplifier is

Assertion (a) : A particle of mass \(m\) dropped into a hole made along the diameter of the earth from one end to the other and possess simple harmonic motion.Reason (R) : Gravitational force between any two particles is inversely proportional to the square of the distance between them.

Two points \(A\) and \(B\) on the axis of a circular current loop are at distances of 4 cm and \(3 \sqrt{3} \mathrm{~cm}\) from the centre of the loop. If the ratio of the induced magnetic fields at points \(A\) and \(B\) is \(216: 125\), the radius of the loop is

A proton and an alpha particle moving with equal speeds enter normally into a uniform magnetic field. The ratio of times taken by the proton and the alpha particle to make one complete revolution in the magnetic field is

A beam of light propagating at an angle \(\alpha_1\) from a medium 1 through to another medium 2 at an angle \(\alpha_2\). If the wavelength of light in medium 1 is \(\lambda_1\), then the wavelength of light in medium \(2,\left(\lambda_2\right)\), is

Two stars of masses ' \(M\) ' and ' \(2 M\) ' that are at a distance ' \(d\) ' apart, are revolving one around another. The angular velocity of the system of two stars is (G-Universal gravitational constant)

In a metre bridge experiment, the ratio of the left gap resistance to right gap resistance is \(2: 3\), the balance point from left is

The speed of sound in air at temperature \(T\) and pressure \(p\) is \(v\). When the temperature is increased to \(2 T\) and the pressure is reduced to \(\frac{p}{2}\), then the speed is changed to

The magnitude of acceleration and velocity of a particle moving in a plane, whose position vector $\overrightarrow{r}=3t^2\hat{\mathrm{i}}+2t\hat{\mathrm{j}}+\hat{\mathrm{k}}$ at $t=2 \sec .$ are, respectively

A circular wire loop of radius, $10 \mathrm{cm}$ carries a total charge of, ${10}^{-5}\mathrm{C}$ distributed uniformly over its length. A small length of, $3.14\times {10}^{-6} \mathrm{m}$ of wire is cut off. The magnitude of the electric field at the centre due to the remaining wire is,
(Assume $\frac{1}{4\pi {ϵ}_0}=9\times {10}^9$ SI units)