Question

A magnetic needle suspended by a silk thread is vibrating in the earth’s magnetic field. If the temperature of the needle is increased by ${500^0}C$ then:
A. The time period decreases
B. The time period remains unchanged
C. The time period increases
D. The needle stops vibrating

Answer 1

Hint: Magnetic needle is a bar magnet, suspended in such a way it shows the direction of the magnetic field of that place. When a magnetic needle is suspended in the magnetic field it performs an angular simple harmonic motion, due to the field and restoring force acts on it.


Complete step by step solution:
The time period of the magnetic needle is given by the following formula.
\[T = 2\pi \sqrt {\dfrac{I}{{mB}}} \]
Here, $T$ is the time period, $I$ is a moment of inertia, $B$ is the magnetic field, and $m$ its magnetic moment.
So, from here we conclude that the time period of the needle is inversely proportional to the strength of the magnetic moment. So, if the magnetic moment increases, the time period of oscillation decreases and vice-versa.
Now, according to the question, the temperature of the needle has increased by 500-degrees. We know that when temperature increases the magnetic moment decreases because due to the increase in the temperature the random motion of the particles increases as a result of the magnetic dipoles moment aligning randomly.
So, as the temperature will increase, the magnetic moment decreases, and due to this the time period of the needle increases.
Hence, the correct option is (C) the time period increases.

Note:
When a magnetic needle is heated to a very high temperature, the magnetic dipole moment decreases as a result the magnetic strength of the needle decreases and the restoring force acting on it also decreases. Hence, the time period increases.