Mass per unit area of a circular disc of radius $$a$$ depends on the distance r from its centre as $$\sigma \left( r \right)$$ = A + Br . The moment of inertia of the disc about the axis, perpendicular to the plane and assing through its centre is:

An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 $$\Omega $$ resistor. The ratio of the currents at time t = $$\infty $$ and at t = 40 s is close to : (Take e² = 7.389)

The electric field of a plane electromagnetic wave is given by
$$\overrightarrow E = {E_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos \left( {kz + \omega t} \right)$$

At t = 0, a positively charged particle is at the point (x, y, z) = $$\left( {0,0,{\pi \over k}} \right)$$.
If its instantaneous velocity at (t = 0) is $${v_0}\widehat k$$ , the force acting on it due to the wave is :

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45^o with the vertical. Then F equal : (Take g = 10 ms^–2 and the rope to be massless)