The magnetic needle of a vibration magnetometer makes `12` oscillations per minute in the horizontal component of earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line it makes `15` oscillations per minute. If the poles of the bar magnet are inter changed, the number of oscillations it takes per minute is

Options

A. `sqrt(61)`
B. `sqrt(63)`
C. `sqrt(65)`
D. `sqrt(67)`

Answer

B

Explanation

`n_(1)=(1)/(2pi)sqrt((MB_(H))/(I)),n_(2)=(1)/(2pi)sqrt((M(B_(H)+B))/(I))` and `n_(3)=(1)/(2pi)sqrt((M(B_(H)-B))/(I))`
where `B` is field strength due to external magnet at the site of magnetic dipole.