A bar magnet is oscillating in the earth's magnetic field with a period T . When the length of the bar magnet is doubled and its mass is quadrupled (while its magnetic moment remains constant), the time period is T₁ . The ratio of T₁ to T is:

Step-by-step solution

Time period: T = 2 I MB_H , where I = ml^2 12 is the moment of inertia. New moment of inertia with m' = 4m and l' = 2l : I' = 4m (2l)^2 12 = 4m 4l^2 12 = 16 ( ml^2 12 ) = 16I Since magnetic moment M remains constant: T₁ = 2 16I MB_H = 4 (2 I MB_H ) = 4T T₁ T = 4 1