A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

An inductance coil has a reactance of 100 $$\Omega $$. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45^o. The self-inductance of the coil is

The figure shows a region of length ‘l’ with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 $$ \times $$ 10⁵ ms^–1 making an angle 60^o with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘l’ is close to
(mass of proton = 1.67 $$ \times $$ 10^–27 kg, charge of the proton = 1.6 $$ \times $$ 10^–19 C)

The displacement time graph of a particle executing S.H.M is given in figure :
(sketch is schematic and not to scale)
Which of the following statements is/are true for this motion?
(A) The force is zero at t = $${{3T} \over 4}$$
(B) The acceleration is maximum at t = T
(C) The speed is maximum at t = $${{T} \over 4}$$
(D) The P.E. is equal to K.E. of the oscillation at t = $${{T} \over 2}$$