Q. 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 interchanged, the number of oscillations it makes per minute is
Explanation
(b) Ist case: $n = \frac{1}{2\pi}\sqrt{\frac{MB_{H}}{I}}$
$\Longrightarrow \ \ \ \ \ n \propto \sqrt{B_{H}} \Longrightarrow \frac{n_{1}}{n_{2}} = \sqrt{\frac{B_{H}}{B_{H} + {B_{H}}_{1}}}$
$\Longrightarrow \ \ \ \frac{12}{15} = \sqrt{\frac{B_{H}}{B_{H} + {B_{H}}_{1}}}$
$\Longrightarrow \ {B_{H}}_{1} = \frac{9}{16}B_{H}$
IInd case:
$\ \ \ \ \ \ \ \ \frac{n_{2}}{n_{3}} = \sqrt{\frac{B_{H} + {B_{H}}_{1}}{B_{H} - {B_{H}}_{1}}}$
$\Longrightarrow \ \frac{15}{n_{3}} = \sqrt{\frac{B_{H} + \frac{9}{16}B_{H}}{B_{H} - \frac{9}{16}B_{H}}}$
$\ \ \ \ \ \ \ \ \frac{15}{n_{3}} = \sqrt{\frac{B_{H} + \frac{9}{16}B_{H}}{B_{H} - \frac{9}{16}B_{H}}}$
$\therefore\ \ \ \ n_{3} = \sqrt{63}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.