નદીમાં પાણીના ઉપરના સ્તરનો વેગ \(36 \,km / h\) છે. જો પાણીના સમક્ષિતિજ સ્તરો વચ્ચે સ્પર્શીય-પ્રતિબળ \(10^{-3} N / m ^{2}\) હોય તો નદીની ઉંડાઈ.......... \(m\) હશે. (પાણીનો શ્યાનતા અંક \(=10^{-2} \,Pa . s\) છે.)

A \(500\)
B \(107\)
C \(700\)
D \(100\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(100\)

Step-by-step Solution

Detailed explanation

\(F =\eta A \frac{\Delta v _{ x }}{\Delta y }\) \(\frac{ F }{ A }=\eta \frac{\Delta v _{ x }}{\Delta y }\) \(\Rightarrow 10^{-3}=10^{-2} \times \frac{36 \times 1000}{ h \times 3600}\) \(\Rightarrow h =10^{-2} \times \frac{36 \times 1000}{10^{-3} \times 3600}=100 \,m\)

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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