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. Motion remains SH with time period = 4T
• B. Motion remains SH and period remains nearly constant
• C. Motion remains SH with time period $= \frac{T}{2}$
• D. Motion remains SH with time period = 2T

Answer 1

Answer: (D)

Motion remains SH with time period = 2T

Answer 2

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 $\frac{T}{T_{2}}=\sqrt{\frac{m}{4 m}}=\frac{1}{2}$
$\therefore T_{2}=2 T$