A proton, a deuteron and an $\alpha$-particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energy. The ratio of the radii of the circular paths described by them is

A magnetic dipole of magnetic moment $6 \times 10^{-2}$ A-m ${ }^2$ and moment of inertia $12 \times 10^{-6} \mathrm{~kg}-\mathrm{m}^2$ performs oscillations in a magnetic field of $2 \times 10^{-2} \mathrm{~T}$. The time taken by the dipole to complete 20 oscillations is ( $\pi \approx 3$ )

A straight wire of length 50 cm carrying a current of 2.5 A is suspended in mid-air by a uniform magnetic field of 0.5 T (as shown in figure). The mass of the wire is ( $g=10 \mathrm{~ms}^{-2}$ )

The magnetic field at the centre of a current carrying loop of radius 0.1 m is $5 \sqrt{5}$ times that at a point along its axis. The distance of this point from the centre of the loop is