A solenoid having area \(A\) and length ' \(l\) ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

Three balls of masses \(2 \mathrm{~kg}, 4 \mathrm{~kg}\) and \(6 \mathrm{~kg}\) respectively are arranged at centre of the edges of an equilateral triangle of side \(2 \mathrm{~m}\). The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be _______\(\mathrm{kg} \mathrm{m}{ }^2\).

Given below are two statements : Statement \(I:\) If the Brewster's angle for the light propagating from air to glass is \(\theta_{ B }\), then Brewster's angle for the light propagating from glass to air is \(\frac{\pi}{2}-\theta_B\). Statement \(II:\) The Brewster's angle for the light propagating from glass to air is \(\tan ^{-1}\left(\mu_{ g }\right)\) where \(\mu_{ g }\) is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below :

As per the given figure, a small ball \(P\) slides down the quadrant of a circle and hits the other ball \(Q\) of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball \(Q\) after collision will be \(............\,m/s\) \(:\left( g =10\,m / s ^2\right)\)

A force \(\left(3 x^2+2 x-5\right) N\) displaces a body from \(\mathrm{x}=2 \mathrm{~m}\) to \(\mathrm{x}=4 \mathrm{~m}\). Work done by this force is _______ J.

The figure shows a Young’s double slit experimental setup. It is observed that when a thin transparent sheet of thickness \(t\) and refractive index \(\mu \) is put in front of one of the slits, the central maximum gets shifted by a distance equal to \(n\) fringe widths. If the wavelength of light used is \(\lambda ,\,t\) will be

A small ball of mass \(m\) and density \(\rho\) is dropped in a viscous liquid of density \(\rho_0\). After sometime, the ball falls with constant velocity. The viscous force on the ball is _______.

A body of mass \(1\,kg\) collides head on elastically with a stationary body of mass \(3\,kg\). After collision, the smaller body reverses its direction of motion and moves with a speed of \(2\,m / s\). The initial speed of the smaller body before collision is \(..........ms ^{-1}\)

The figure gives experimentally measured \(\mathrm{B}\) vs. \(H\) variation in a ferromagnetic material. The retentivity, co-ercivity and saturation. respectively, of the material are

A \(1\,m\) long metal rod \(XY\) completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \(0.15\,T\). If the resistance of the circuit is \(5\,\Omega\), the force needed to move the rod in direction, as indicated, with a constant speed of \(4\,m / s\) will be \(................\,10^{-3}\,N\)

A particle moving in a straight line covers half the distance with speed \(6 \mathrm{~m} / \mathrm{s}\). The other half is covered in two equal time intervals with speeds 9 \(\mathrm{m} / \mathrm{s}\) and \(15 \mathrm{~m} / \mathrm{s}\) respectively. The average speed of the particle during the motion is _______.

A zener diode having zener voltage \(8\, {V}\) and power dissipation rating of \(0.5\, {W}\) is connected across a potential divide arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance \({R}_{{p}}\) is \(....\,\Omega\)