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-- Two geometrically similar magnets having same mass but magnetic moments M1 and M2 (M1 > M2) are taken and vibrate in a vibration magnetometer with their like poles together and unlike poles together. If the ratio of their time periods in both cases respectively is 1/2, then ratio of M1 to M2 is:
A
15/17
B
17/15
C
12/13
D
13/12
Explanation
T1/T2 = √[(M1-M2)/(M1+M2)]. (1/2)^2 = (M1-M2)/(M1+M2) => 1/4 = (M1-M2)/(M1+M2). M1+M2 = 4M1 - 4M2 => 5M2 = 3M1 => M1/M2 = 5/3? Let's re-read ratio: 1/4 (from image). (1/4)^2 = 1/16. M1+M2 = 16M1 - 16M2 => 17M2 = 15M1 => M1/M2 = 17/15.
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