A bar magnet is oscillating in the earth's magnetic field with a period T . What happens to its period and motion, if its mass is quadrupled?

Step-by-step solution

The time period T of a bar magnet oscillating in a uniform magnetic field B is given by the formula T = 2 I MB , where I is the moment of inertia of the magnet and M is its magnetic dipole moment. For a bar magnet of mass m , length l , and width w , the moment of inertia about the axis of oscillation is I = m(l^2 + w^2) 12 . When the mass is quadrupled, the new mass m' = 4m . Assuming the dimensions of the magnet remain unchanged, the new moment of inertia becomes I' = (4m)(l^2 + w^2) 12 = 4I . The new time period