Question

A bar magnet is oscillating in the Earth's magnetic field with a period T. What happens to this period and motion if this mass is quadrupled:

• A. Motion remains S.H. with time period = $\frac T2$
• B. Motion remains S.H. with time period = 2T
• C. Motion remains S.H. with time period = 4T
• D. Motion remains S.H. with time and period remains nearly constant

Answer 1

Answer: (B)

Motion remains S.H. with time period = 2T

Answer 2

Initial mass of the magnet m1 = m and final mass of the magnet m2 = 4 m.
The time period $T = 2\pi \sqrt {\frac {I}{MB}}$

$T = 2\pi \sqrt {\frac {mk^2}{MB}}$

⇒ $T ∝ \sqrt {m}$
Therefore,

$\frac {T_1}{T_2} = \sqrt {\frac {m_1}{m_2}}$

$\frac {T_1}{T_2} = \sqrt {\frac {m}{4m}}$

$\frac {T_1}{T_2} = \frac 12$

$T_2 = 2T_1$

$T_2 = 2T$

So, the correct option is (B): Motion remains S.H. with time period = 2T