A thin magnet of magnetic moment M and moment of inertia I oscillates with small amplitude in a uniform magnetic field B and has time period T. It is then bent uniformly into a semicircular arc. Assume its moment of inertia about the suspension axis remains equal to I.
The new time period is:

Question

A thin magnet of magnetic moment M and moment of inertia I oscillates with small amplitude in a uniform magnetic field B and has time period T. It is then bent uniformly into a semicircular arc. Assume its moment of inertia about the suspension axis remains equal to I.

The new time period is:

G1 Physics · Accepted Answer

Initially, T = 2π√(I/MB). After bending into a semicircle, M' = 2M/π. The moment of inertia and magnetic field are unchanged. Hence, T' = 2π√[I/(M'B)]. Therefore, T'/T = √(M/M') = √[M/(2M/π)] = √(π/2). Thus, T' = T√(π/2).