Question:
A bar magnet is oscillating in the earth's magnetic field with a period $T$. What happens to its period and motion if its mass is quadrupled?
A bar magnet is oscillating in the earth's magnetic field with a period $T$. What happens to its period and motion if its mass is quadrupled?
Updated On: May 21, 2024
- Motion remains SH with time period = 4T
- Motion remains SH and period remains nearly constant
- Motion remains SH with time period $ = \frac{T}{2} $
- Motion remains SH with time period = 2T
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The Correct Option is D
Solution and Explanation
The time period will be
$ T=2 \pi \sqrt{\mid \frac{\theta}{\alpha}} \mid $
$=2 \pi \sqrt{\frac{I}{M H}}$
or $T \propto \sqrt{I} $
or $T \propto \sqrt{m} $
$\left(\therefore I=\frac{m l^{2}}{12}\right) $
$\therefore \frac{T_{1}}{T_{2}}=\sqrt{\frac{m_{1}}{m_{2}}} $
or $\frac{T}{T_{2}}=\sqrt{\frac{m}{4 m}}=\frac{1}{2} $
$\therefore T_{2}=2 T$
$ T=2 \pi \sqrt{\mid \frac{\theta}{\alpha}} \mid $
$=2 \pi \sqrt{\frac{I}{M H}}$
or $T \propto \sqrt{I} $
or $T \propto \sqrt{m} $
$\left(\therefore I=\frac{m l^{2}}{12}\right) $
$\therefore \frac{T_{1}}{T_{2}}=\sqrt{\frac{m_{1}}{m_{2}}} $
or $\frac{T}{T_{2}}=\sqrt{\frac{m}{4 m}}=\frac{1}{2} $
$\therefore T_{2}=2 T$
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Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
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Some of the properties of the magnetic field lines are:
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