Question

The time period of a bar magnet suspended horizontally in the earth's magnetic field and allowed to oscillate
A. Is directly proportional to the square root of its mass
B. Is directly proportional to its pole strength
C. Is inversely proportional to its magnetic moment
D. Decreases if the length increases but pole strength remains same

Answer 1

Hint:The length of time it takes for something to complete one oscillation is known as its time period. Normally, we can calculate frequency from angular velocity, and once we have calculated frequency, the inverse of that frequency provides us the time period. If an object is moving in a simple harmonic manner, the restoring force is found first, and the time period is calculated from there.

Formula used:
The time period for an oscillating bar magnet hanging horizontally in the geomagnetic field is given by:
$\mathrm{T}=2 \pi \sqrt{\dfrac{(\mathrm{I})}{(\mathrm{M}) \mathrm{B}_{\mathrm{H}}}}$
Here, $M$ is the magnetic moment, $B_H$ is the horizontal component of the magnetic field and $I$ is the moment of inertia.

Complete step by step solution:
We are aware that the time period for an oscillating bar magnet hanging horizontally in the geomagnetic field is given by:
$\mathrm{T}=2 \pi \sqrt{\dfrac{(\mathrm{I})}{(\mathrm{M}) \mathrm{B}_{\mathrm{H}}}}$
A magnetic moment, also referred to as a magnetic dipole moment, is a measurement of an object's tendency to align with a magnetic field. A vector quantity is the magnetic moment.

The magnetic moment vector frequently aligns with the magnetic field lines when the objects are positioned in that way. A magnet's magnetic moment is directed from its southern to northern poles. The magnetic field that a magnet creates is inversely related to its magnetic moment.
$\mathrm{T} \propto \dfrac{1}{\sqrt{\mathrm{M}}}$
Then it is inversely proportional to its magnetic moment.

Hence, the correct answer is option C.

Note: Oscillation is the continual transition of an object between two states or positions. It is also known as the periodic motion because it tends to repeat itself in predictable cycles. As an illustration, consider a sine wave with a side-to-side pendulum swing or an up-and-down motion with a spring's weight. The oscillating movement revolves around a mean value or an equilibrium point. The periodic motion is another name for this movement. Whether it is an up-down movement or a side-to-side movement, a single oscillation is regarded as a whole movement throughout time.