At places `A` and `B` using vibrating magnetometre, a magnet vibrates in a horizontal plane and its respective periodic time are 2 sec and 3 sec and at these places the earth's horizontal components are `H_(A)` and `H_(B)` respectively. Then the ratio between `H_(A)` and `H_(B)` will be

Options

A. `9:4`
B. `3:2`
C. `4:9`
D. `2:3`

Answer

A

Explanation

`T=2pisqrt(I/(MH))implies T prop 1/sqrt(H)impliesT_(A)/T_(B)=sqrt(H_(B)/H_(A))`
`implies H_(A)/H_(B)=(T_(B)/T_(A))^(2)=(3/2)^(2)=9/4`.