Consider a circular loop that is uniformly charged and has a radius \(\mathrm{a} \sqrt{2}\). Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

\(7\) mole of certain monoatomic ideal gas undergoes a temperature increase of \(40 K\) at constant pressure. The increase in the internal energy of the gas in this process is\(....J\) (Given \(R =8.3 JK ^{-1} mol ^{-1}\) )

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of \(25 \pi \mathrm{Nm}\) for 40 s, the speed increases to 2100 rpm. The diameter of the disk is ________ m.

An object of mass \(5\, kg\) is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of \(10\, N\) throughout the motion. The ratio of time of ascent to the time of descent will be equal to \(\left[\right.\)Use \(g =10 \,ms ^{-2}]\)

If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\)____________

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is ___________ mV.

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is \(\frac{x}{2} M L^2 kg m ^2\). The value of \(x\) is _________.

A circular loop of radius \(r\) is carrying current I A. The ratio of magnetic field at the centre of circular loop and at a distance \(r\) from the center of the loop on its axis is:

Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of the badminton racket are same \((M)\) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \(\frac{r}{2}\) distance from the end \(A\) of the handle will be ....... \(Mr^2\)?

The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of \(3 rd\) orbit will be \(.........R\)

A ray of light of intensity \(I\) is incident on a parallel glass slab at point \(A\) as shown in diagram. It undergoes partial reflection and refraction. At each reflection, \(25\%\) of incident energy is reflected. The rays \(AB\) and \(A'B'\) undergo interference. The ratio of \(I_{max}\) and \(I_{min}\) is