\(1 \,m \) લંબાઈવાળું એક સાદુ લોલક \(10 \,rad/s\) કોણીય આવૃત્તિથી દોલન કરે છે. લોલકનો આધાર \(1 \,rad/s\) જેટલી નાની કોણીય આવૃત્તિ અને \(10^{-2}\, m\) જેટલા કંપવિસ્તારથી ઉપર નીચે દોલન કરવાનું શરૂ કરે છે. લોલકની કોણીય આવૃત્તિમાં થતા સાપેક્ષ ફેરફારને _______ દ્વારા સચોટ રીતે દર્શાવી શકાય

A \(10^{-3} rad/s\)
B \(1\,rad/s\)
C \(10^{-1} rad/s\)
D \(10^{-5} rad/s\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(10^{-3} rad/s\)

Step-by-step Solution

Detailed explanation

Angular frequency of pendulum \(\omega \propto \sqrt{\frac{g_{e f f}}{\ell}}\) \(\therefore \quad \frac{\Delta \omega}{\omega}=\frac{1}{2} \frac{\Delta g_{e f f}}{g_{e f f}}\) \(\Delta \omega=\frac{1}{2} \frac{\Delta g}{g} \times \omega\) \([ \omega_{s}=\) angular frequency of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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