ત્રિજ્યા \(r\) અને ઘનતા \(\sigma\) ધરાવતો એક ગોળાકાર પદાર્થ ઘનતા \(\rho\) અને શ્યાનતા \(\eta\) ધરાવતા શ્યાન પ્રવાહીમાંથી મુક્તપણે પસાર થાય છે અને અંતિમ વેગ \(v _0\) પ્રાપ્ત કરે છે. રાશિ \(\eta\) માં અંદાજિત મહત્તમ ત્રુટિ હશે: (\(\sigma, \rho\) અને g (ગુરુત્વાકર્ષી પ્રવેગ) સાથે સંકળાયેલ ત્રુટિઓને અવગણો)

A \(2 \frac{\Delta r }{ r }-\frac{\Delta v _0}{ v _0}\)
B \(\frac{2 \Delta r }{ r }+\frac{\Delta v _0}{ v _0}\)
C \(2\left[\frac{\Delta r }{ r }+\frac{\Delta v _0}{ v _0}\right]\)
D \(2\left[\frac{\Delta r }{ r }-\frac{\Delta v _0}{ v _0}\right]\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2 \Delta r }{ r }+\frac{\Delta v _0}{ v _0}\)

Step-by-step Solution

Detailed explanation

\(v _0=\frac{2}{9} \frac{ r ^2 g}{ n }\left(\rho_{ B }-\rho_{ L }\right)\) \(n =\frac{2}{9} \frac{ r ^2 g}{ v _0}\left(\rho_{ B }-\rho_{ L }\right)\) \(\frac{\Delta n }{ Il }=\frac{2 \Delta r }{ r }+\frac{\Delta v _0}{ v _0}\)

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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