A long straight wire with a circular crosssection having radius \(R\), is carrying a steady current \(I\). The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance \(r\;( r < R )\) from its centre will be

Given the masses of various atomic particles \(m _{ p }=1.0072 u , m _{ n }=1.0087 u\) \(m _{ e }=0.000548 u , m _{ v }=0, m _{ d }=2.0141 u\) where \(p \equiv\) proton, \(n \equiv\) neutron, \(e \equiv\) electron, \(\overline{ v } \equiv\) antineutrino and \(d \equiv\) deuteron. Which of the following process is allowed by momentum and energy conservation \(?\)

An electron is moving along \(+x\) direction with a velocity of \(6 \times 10^{6}\, ms ^{-1}\). It enters a region of uniform electric field of \(300 \,V / cm\) pointing along \(+ y\) direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the \(x\) direction will be

A projectile is given an initial velocity of \((\hat i + 2\hat j)\ ms^{-1}\), where \(\hat i\) is along the ground and \(\hat j\) is along the vertical. If \(g = 10\ m/s^2\) , the equation of its trajectory is

A thin rod of mass \(0.9\, kg\) and length \(1 \,m\) is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move \(0.1\, kg\) moving in a straight line with velocity \(80\,m / s\) hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in \(rad/s\)) of the rod immediately after the collision will be

In Young's double slit experiment, the distance between slits and the screen is \(1 .0\,\,m\) and monochromatic light of \(600\,\,nm\)  is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance \(d_0\) between the slits . If the angular resolution of the eye is \(\frac {1}{60}^o,\) the value of \(d_0\)  is close to......\(mm\)

In the following circuit, the reading of the ammeter will be : (Take Zener breakdown voltage \(=4 \mathrm{~V})\)

In a Young's double slit experiment, light of \(500\, nm\) is used to produce an interference pattern. When the distance between the slits is \(0.05\, mm\), the angular width (in degree) of the fringes formed on the distance screen is close to\(........^o\)

In a physical balance working on the principle of moments, when \(5\, mg\) weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

The coercivity of a magnet is \(5 \times 10^3 \mathrm{~A} / \mathrm{m}\). The amount of current required to be passed in a solenord of length \(30 \mathrm{~cm}\) and the number of turns \(150\) , so that the magnet gets demagnetised when inside the solenoid is _______ A.

The masses and radii of the earth and moon are \(\left({M}_{1}, {R}_{1}\right)\) and \(\left({M}_{2}, {R}_{2}\right)\) respectively. Their centres are at a distance ' \({r}\) ' apart. Find the minimum escape velocity for a particle of mass ' \({m}\) ' to be projected from the middle of these two masses:

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as \(100\) Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by \(30^{\circ}\) in clockwise direction, the intensity of emerging light will be .......... Lumens.

If \({R}_{{E}}\) be the radius of Earth, then the ratio between the acceleration due to gravity at a depth \(' {r} '\) below and a height \(' r '\) above the earth surface is: (Given : \(\left.{r}<{R}_{{E}}\right)\)