The periodic time of a magnet in vibration magnetometer is $T_0$. If a magnet is replaced by another magnet whose moment of inertia is three times and magnetic moment is one-third of the original magnet, then time period of new magnet will be

A square loop ABCD of side L carrying a current $I_1$ is placed at a distance $(L/3)$ from a conductor coplaner with a straight conductor XY carrying current $I_2$ as shown in figure. The net force on the loop will be ($\mu_0$ = magnetic permeability)

A long solenoid carrying a current produces a magnetic field '$B$' along its axis. If the currunt is tripled and the number of turns per cm is halved then new value of magnetic field will be

The self inductance of an air-core inductor (solenoid) is $0.03$ mH. By introducing an iron core into inductor the self-inductance increases to $30$ mH. The relative permeability of the core used is