A parallel plate capacitor has a capacitance \(\mathrm{C}=200 \mathrm{pF}\). It is connected to \(230 \mathrm{~V}\) ac supply with an angular frequency \(300 \mathrm{rad} / \mathrm{s}\). The \(\mathrm{rms}\) value of conduction current in the circuit and displacement current in the capacitor respectively are _______.

A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just \(10 \%\) of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is.....\(^o\)

The position of an object having mass \(0.1\) kg as a function of time \(t\) is given as \(\vec{r} = \left(10t^2\hat{i} + 5t^3\hat{j}\right)\) m. At \(t = 1\) s, which of the following statements are correct?
A. The linear momentum \(\vec{p} = \left(2\hat{i} + 1.5\hat{j}\right)\) kg·m/s.
B. The force acting on the object \(\vec{F} = \left(2\hat{i} + 3\hat{j}\right)\) N.
C. The angular momentum of the object about its origin \(\vec{L} = 15\hat{k}\) J·s.
D. The torque acting on the object about its origin \(\vec{\tau} = 20\hat{k}\) N·m.
Choose the correct answer from the options given below :

The coefficient of static friction between a wooden block of mass \(0.5\, kg\) and a vertical rough wall is \(0.2\) The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be \(N\) \(\left[ g =10\, ms ^{-2}\right]\)

A solid sphere of radius \(r\) made of a soft material of bulk modulus \(K\) is surrounded by a liquid in a cylindrical container. A massless piston of area \(a\) floats on the surface of the liquid, covering entire crosssection of cylindrical container. When a mass \(m\) is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \(\left( {\frac{{dr}}{r}} \right)\) is 

A slender uniform rod of mass \(M\) and length \(l\) is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle \(\theta\) with the vertical is

A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\)

Electric field in a region is given by \( \vec{E}=Ax\hat{i}+By\hat{j} \), where \( A=10~V/m^{2} \) and \( B=5~V/m^{2} \). If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is __________ V.

In a nuclear fission process, a high mass nuclide \((A \approx 236)\) with binding energy \(7.6\  \mathrm{MeV} /\) Nucleon dissociated into middle mass nuclides \((A \approx 118)\), having binding energy of \(8.6 \ \mathrm{MeV} / \mathrm{Nucleon}\). The energy released in the process would be \(\mathrm{MeV}\).

Two plane polarized light waves combine at a certain point whose electric field components are :
\(\begin{aligned} & \mathrm{E}_1=\mathrm{E}_0 \sin \omega \mathrm{t} \\ & \mathrm{E}_2=\mathrm{E}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)\end{aligned}\)
Find the amplitude of the resultant wave.

A car accelerates from rest to \(u\,m / s\). The energy spent in this process is \(E\,J\). The energy required to accelerate the car from \(u\,m / s\) to \(2u\,m / s\) is \(nE\,J\). The value of \(n\) is ..............

A light whose electric field vectors are completely removed by using a good Polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

If we need a magnification of \(375\) from a compound microscope of tube length \(150\; \mathrm{mm}\) and an objective of focal length \(5\; \mathrm{mm}\), the focal length of the eye-piece, should be close to.....\(mm\)