A square current carrying loop made of thin wire and having a mass `m=10g` can rotate without friction with respect to the vertical axis `OO'` passing through the centre of the loop at right angles to two opposite sides of the loop.The loop is placed in a homogeneous magnetic field with an induction `B=10^(-1)T` directed at right angles to the plane of the drawing.A current `I=2A` is flowing in the loop.Find the period of small oscillations that the loop perfoms about its position of stable equilibrium.

Explanation

`T_0 = 2pi sqrt(m)/(6IB) = 0.57 s`
[Hint : Restoring torque equation :
`I AB sin theta = - I_0 theta,` where `A = a^2`
and `I_0 = m/4 [(a^2)/(12) xx 2 + (a/2)^2 xx 2 ]`
`= m /4 xx 2/3 a^2`
`rarr (m/6 a^2) overset(..)theta = -a^2 B theta rArr overset(..) = - ((6IB)/(M)) theta ]`.