Two discs have moments of inertia I₁ and I₂ about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $$\omega$$₁ and $$\omega$$₂ respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :

Three capacitors C₁ = 2$$\mu$$F, C₂ = 6$$\mu$$F and C₃ = 12$$\mu$$F are connected as shown in figure. Find the ratio of the charges on capacitors C₁, C₂ and C₃ respectively :

if the rms speed of oxygen molecules at 0$$^\circ$$C is 160 m/s, find the rms speed of hydrogen molecules at 0$$^\circ$$C.

A constant magnetic field of 1T is applied in the x > 0 region. A metallic circular ring of radius 1m is moving with a constant velocity of 1 m/s along the x-axis. At t = 0s, the centre of O of the ring is at x = $$-$$1m. What will be the value of the induced emf in the ring at t = 1s? (Assume the velocity of the ring does not change.)