In a vibration magnetometer, the time period of a bar magnet oscillating in horizontal componnt of earth's magnetic field is `2 sec`. When a magnet is brought near and parallel to it, the time period reduces to `1 sec`. The ratio `H//F` of the horizontal component `H` and the field `F` due to magnet will be

Options

A. 3
B. `1//3`
C. `sqrt3`
D. `1//sqrt3`

Answer

b

Explanation

(b) `T prop (1)/(sqrtH) rArr (T_(1))/(T_(2))=sqrt((H_(2)/(H_(1)) rArr (2)/(1) =sqrt((H+F)/(H)))`
`rArr F=3H"or"(H)/(F)=(1)/(3)`