With a standard rectangular bar magnet of length (l), breadth (b ; b< < l) and magnetic moment M , the time period of the magnet in a vibration magnetometer is 4 ~s . If the magnet is cut normal to its length into four equal pieces, the time period (in seconds) with one of the pieces is

Step-by-step solution

Time period of magnet in vibration magnetometer, T=2 1 M H where, I= moment of inertia of magnet M= magnetic moment H= horizontal component of earth's magnetic field aligned & T₁ T₂ = I₁ I₂ M₂ M₁ & 4 T₂ = m l^2 / 12 m / 4(l / 4)^2 / 12 & = 4 16 12 12 4 = 16 & 4 T₂ =4 & T₂=1 ~s & aligned