A ring is hung on a nail. It can oscillate, without slipping or sliding
(i) in its plane with a time period T₁ and,
(ii) back and forth in a direction perpendicular to its plane,
with a period T₂. The ratio $${{{T_1}} \over {{T_2}}}$$ will be :

An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length $$l$$ and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is :

An iron rod of volume 10^–3 m³ and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be :

In an experiment to verify Stokes law, a small spherical ball of radius r and density $$\rho $$ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to :
(ignore viscosity of air)