MHT CET · Physics · Oscillations
Two simple harmonic motions of angular frequency 100 and \(1000 \mathrm{rad} \mathrm{s}^{-1}\) have the same displacement amplitude. The ratio of their maximum acceleration is
- A \(1: 10\)
- B \(1: 10^{2}\)
- C \(1: 10^{3}\)
- D \(1: 10^{4}\)
Answer & Solution
Correct Answer
(B) \(1: 10^{2}\)
Step-by-step Solution
Detailed explanation
Acceleration of simple harmonic motion is
\(a_{\max }=-\omega^{2} A \)
\( \text { or } \frac{\left(a_{\max }\right)_{1}}{\left(a_{\max }\right)_{2}}=\frac{\omega_{1}^{2}}{\omega_{2}^{2}} \text { (as A remains same) } \)
\( \text { or } \frac{\left(a_{\max }\right)_{1}}{\left(a_{\max }\right)_{2}}=\frac{(100)^{2}}{(1000)^{2}}=\left(\frac{1}{10}\right)^{2} \)
\(=1: 10^{2}\)
\(a_{\max }=-\omega^{2} A \)
\( \text { or } \frac{\left(a_{\max }\right)_{1}}{\left(a_{\max }\right)_{2}}=\frac{\omega_{1}^{2}}{\omega_{2}^{2}} \text { (as A remains same) } \)
\( \text { or } \frac{\left(a_{\max }\right)_{1}}{\left(a_{\max }\right)_{2}}=\frac{(100)^{2}}{(1000)^{2}}=\left(\frac{1}{10}\right)^{2} \)
\(=1: 10^{2}\)
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