Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles togather, 12 oscillations per minute are made but for unlike poles togather only 4 oscillations per minute are axecuted. The ratio of their magnetic miments is

Options

A. `3:1`
B. `1:3`
C. `3:5`
D. `5: 4`

Answer

D

Explanation

`T prop (1)/(sqrtM) rArr f prop sqrtM`
`(f_(1))/(f_(2))= sqrt((M_(1) + M_(2))/(M_(1)- M_(2))) rArr (f_(1)^(2))/(f_(2)^(2))= (M_(1) + M_(2))/(M_(1) - M_(2))`
`rArr (f_(1)^(2))/(f_(2)^(2))= ((M_(1))/(M_(2)) +1)/((M_(1))/(M_(2))-1) rArr (f_(1)^(2))/(f_(2)^(2)) (M_(1))/(M_(2))- (f_(1)^(2))/(f_(2)^(2)) = (M_(1))/(M_(2)) + 1`
`rArr (M_(1))/(M_(2)) [(f_(1)^(2))/(f_(2)^(2))-1] = 1+ (f_(1)^(2))/(f_(2)^(2))`
`rArr (M_(1))/(M_(2))= (f_(1)^(2) + f_(2)^(2))/(f_(1)^(2)- f_(2)^(2)) = (((12)/(60))^(2) + ((4)/(60))^(2))/(((12)/(60))^(2) - ((4)/(60))^(2)) rArr (M_(1))/(M_(2))= (5)/(4)`