એક કણ \(A\) જેટલા કંપવિસ્તારથી સરળ આવર્તગતિ કરે છે.કણ જયારે તેની સરેરાશ અવસ્થાની \(\frac{{2A}}{3}\) જેટલા અંતરે હોય છે,ત્યારે અચાનક તેની ઝડપ ત્રણ ગણી કરી દેવામાં આવે છે.કણનો નવો કંપવિસ્તાર છે:

A \(A\)\(\sqrt 3 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\)
B \(\;\frac{{7A}}{3}\)
C \(\;\frac{A}{3}\sqrt {41} \)
D \(3A\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\;\frac{{7A}}{3}\)

Step-by-step Solution

Detailed explanation

Let new amplitude is \(A'\) initial velocity \(v^{2}=\omega^{2}\left(A^{2}-\left(\frac{2 A}{3}\right)^{2}\right)\) \(...(1)\) Where \(A\) is initial amplitude \(\&\, \omega\) is angular frequency. Final velocity…

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.

Same subject

યાદી - I ને યાદી - II સાથે જોડો.

યાદી - I	યાદી - II
(A) શૂન્યાવકાશની પરમિએબિલિટી	(I) \(\left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)
(B) ચુંબકીય ક્ષેત્ર	(II) \(\left[\mathrm{M} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\)
(C) ચુંબકીય મોમેન્ટ	(III) \(\left[\mathrm{M} \mathrm{~L} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]\)
(D) વળ અચળાંક	(IV) \(\left[\mathrm{L}^2 \mathrm{~A}\right]\)

નીચે\(\text{ }\)આપેલા\(\text{ }\)વિકલ્પોમાંથી\(\text{ }\)સાચો\(\text{ }\)જવાબ\(\text{ }\)પસંદ\(\text{ }\)કરો\(\text{ }\):

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