Question

The frequency of oscillation of a small magnet in a magnetic field of induction 'B' is '\(n\)'. If the frequency of oscillations of the same magnet in a field of induction 'X' falls to \((\frac{n}{3})\), the value of 'X' is

• A. \(3B\)
• B. \(9B\)
• C. \(\frac{B}{3}\)
• D. \(\frac{B}{9}\)

Hint:

Frequency of a magnet oscillating in a field varies as the square root of B.

Answer 1

The Correct Option is D

Step 1: Proportion:
Since $f^2\propto B$, squaring the frequency ratio gives the field ratio.

Step 2: Compute:
$\left(\dfrac13\right)^2=\dfrac19$. So $X=\dfrac B9$.

Step 3: Answer:
Option (D).

Final Answer:
Option (D). \[ \boxed{\text{(D) } \frac{B}{9}} \]