Question

Two simple harmonic motions of angular frequency \(300 \mathrm{rad} / \mathrm{s}\) and \(3000 \mathrm{rad} / \mathrm{s}\) have same amplitude. The ratio of their maximum accelerations is

• A. \(1:10\)
• B. \(1:10^{2}\)
• C. \(1:10^{3}\)
• D. \(1:10^{4}\)

Hint:

Maximum acceleration in SHM is the square of the angular frequency times the amplitude.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In SHM the maximum acceleration is \(a_{max}=\omega^{2}A\).
Both motions have the same amplitude, so the ratio depends only on \(\omega^{2}\).

Step 2: Calculation
\(\dfrac{a_1}{a_2}=\dfrac{\omega_1^{2}}{\omega_2^{2}}=\left(\dfrac{300}{3000}\right)^{2}=\left(\dfrac{1}{10}\right)^{2}\)

Step 3: Compare the options
The ratio is \(1:10^{2}\), which matches option (B).

Final Answer:
The ratio of the maximum accelerations is 1 : 100. \[ \boxed{\text{(B) }1:10^{2}} \]