એક સાદા લોલકના ધાત્વીય દોલકની સાપેક્ષ ધનતા \(5\) છે. આ લોલકનો આવર્તકાળ \(10\,s\) છે. જો ધાત્વીય દોલકને પાણીમાં ડૂબાડવામાં આવે તો નવો આવર્તકાળ \(5 \sqrt{x} s\) જેટલો થાય છે.\(x\) નું મૂલ્ય \(....\) થશે.

A \(4\)
B \(5\)
C \(3\)
D \(0\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(5\)

Step-by-step Solution

Detailed explanation

\(g^{\prime}=\frac{m g-F_{B}}{m}\) \(=\frac{\rho_{B} V g-\rho_{\pi} V g}{\rho_{B} V}\) \(=\left(\frac{\rho_{B}-\rho_{\pi}}{\rho_{B}}\right) g \quad T=2 \pi \sqrt{\frac{\ell}{g}}\) \(=\frac{5-1}{5} \times g\) \(=\frac{4}{5} g\)…

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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લિસ્ટ \(-I\) ને લિસ્ટ \(-II\) સાથે સરખાવો

લિસ્ટ \(-I\)	લિસ્ટ \(-II\)
\((a)\) ટોર્ક	\((i)\) \({MLT}^{-1}\)
\((b)\) બળનો આઘાત	\((ii)\) \({MT}^{-2}\)
\((c)\) તણાવ	\((iii)\) \({ML}^{2} {T}^{-2}\)
\((d)\) પૃષ્ઠતાણ	\((iv)\) \({MI} {T}^{-2}\)

નીચે આપેલા વિકલ્પોમાંથી સાચો જવાબ પસંદ કરો.

JEE Mains 2021 Medium

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