\(0.3\; \mathrm{m}\) લંબાઈના તારના એક છેડે \(\mathrm{m}=10\; \mathrm{kg}\) નો પદાર્થ બાંધેલો છે.તેને અવકાશમાં મહત્તમ કેટલી કોણીય ઝડપથી(\(rad \;s^{-1}\) માં) ફેરવી શકાય?(તારનું મહત્તમ બ્રેકિંગ પ્રતિબળ \(=4.8 \times 10^{7} \;\mathrm{Nm}^{-2}\) અને તારના આડછેડનું ક્ષેત્રફળ \(=10^{-2}\; \mathrm{cm}^{2}\) છે)

A \(8\)
B \(7\)
C \(11\)
D \(4\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(4\)

Step-by-step Solution

Detailed explanation

\(\mathrm{T}=\mathrm{m\omega}^{2} \ell\) Breaking stress \(=\frac{\mathrm{T}}{\mathrm{A}}=\frac{\mathrm{mo}^{2} \ell}{\mathrm{A}}\) \(\Rightarrow \omega^{2}=\frac{4.8 \times 10^{7} \times\left(10^{-2} \times 10^{-4}\right)}{10 \times 0.3}=16\) \(\Rightarrow \omega=4\)

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

સૂચિ \(I\) ને સૂચિ \(II\) સાથે જોડો

સૂચિ - \(I\)	સૂચિ - \(II\)
\((A)\) ટૉર્ક	\((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\)
\((B)\) ચુંબકીય ક્ષેત્ર	\((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\)
\((C)\) ચુંબકીય ચાકમાત્રા	\((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\)
\((D)\) મુક્ત અવકાશની પારગમ્યતા	\((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)

નીચે આપેલા વિકલ્પોમાંથી સાચો જવાબ પસંદ કરો :

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