At very high frequencies, the effective impendance of the given circuit will be \(....\Omega\)

Light enters from air into a given medium at an angle of \(45^{\circ}\) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \(15^{\circ}\) from its original direction. The refractive index of the medium is.

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius \(2.0 \times 10^{-5}\, {m}\) and density \(1.2 \times 10^{3} \,{kgm}^{-3}\) ? Take viscosity of liquid \(=1.8 \times 10^{-5}\, {Nsm}^{-2} .\) (Neglect buoyancy due to air).

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below: \({ }_{1}^{2} X +{ }_{1}^{2} X ={ }_{2}^{4} Y\) The binding energies per nucleon \({ }_{1}^{2} X\) and \({ }_{2}^{4} Y\) are \(1.1\,MeV\) and \(7.6\,MeV\) respectively. The energy released in this process is \(MeV\).

A physical quantity C is related to four other quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s as follows \(\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}\)
The percentage errors in the measurement of \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are \(1 \%, 2 \% 3 \%\) and \(2 \%\) respectively. The percentage error in the measurement of C will be _____\(\%\).

A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that \(\theta(t)=5 t^2-8 t\), where \(\theta(t)\) is the angular position of the rotating disc as a function of time \(t\). How much power is delivered by the applied torque, when \(t=2 s\) ?

A square loop of edge length \(2 \mathrm{~m}\) carrying current of \(2 \mathrm{~A}\) is placed with its edges parallel to the \(\mathrm{x}-\mathrm{y}\) axis. A magnetic field is passing through the \(x-y\) plane and expressed as \(\vec{B}=B_0(1+4 x) \hat{k}\), where \(\mathrm{B}_0=5 \mathrm{~T}\). The net magnetic force experienced by the loop is _______ \(\mathrm{N}\).

Given below are two statements: Statement \(I:\) Rotation of the earth shows effect on the value of acceleration due to gravity \((g)\). Statement \(II:\) The effect of rotation of the earth on the value of \(g\) at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below.

Two light identical springs of spring constant \(k\) are attached horizontally at the two ends of a uniform horizontal rod \(AB\) of length \(l\) and mass \(m\). the rod is pivoted at its centre \(‘O’\) and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is

If electronic charge \(e\), electron mass \(m\), speed of light in vacuum \(c\) and Planck 's constant \(h\) are taken as fundamental quantities, the permeability of vacuum \(\mu _0\) can be expressed in units of

The figure shows a square loop \(L\) of side \(5\, cm\) which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of \(1\, cms^{-1}\). At some instant, a part of \(L\) is in a uniform magnetic field of \(1\, T\), perpendicular to the plane of the loop. If the resistance of \(L\) is \(1.7\,\Omega \), the current in the loop at that instant will be close to.....\(\mu A\)

An electric dipole is formed by two equal and opposite charges \(q\) with separation \(d\). The charges the same mass \(m\). It is kept in a uniform electric field \(E\). If it slightly rotated from its equilibrium orientation, then its angular frequency \(\omega \) is

To establish an instantaneous current of \(2\,A\) through a \(1\,\mu F\) capacitor ; the potential difference across the capacitor plates should be changed at the rate of