તમે એક ઓલિક ઍસિડનું મંદ દ્રાવણ લીધું છે કે જેમાં પ્રતિ \(cm ^{3}\) દ્રાવણમાં ઓલિક ઍસિડનું પ્રમાણ \(0.01 \,cm ^{3}\) છે. \(\left(\frac{3}{40 \pi}\right)^{\frac{1}{3}} \times 10^{-3}\; cm\) ત્રિજ્યાના દ્રાવણના \(100\) ટીપાંથી \(4\;cm ^{2}\) ક્ષેત્રફળ ધરાવતું પાતળું સ્તર બનાવવામાં આવે છે. તેમાં ઓલિક એસિડની જાડાઈ \(x \times 10^{-14} \;m\) છે. જ્યાં \(x\) કેટલું હશે?

A \(30\)
B \(25\)
C \(20\)
D \(36\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(25\)

Step-by-step Solution

Detailed explanation

\(4 t _{ T }=100 \times \frac{4}{3} \pi r ^{3}\) \(=100 \times \frac{4 \pi}{3} \times \frac{3}{40 \pi} \times 10^{-9}=10^{-8}\, cm ^{3}\) \(t _{ T }=25 \times 10^{-10}\, cm\) \(=25 \times 10^{-12} \,m\) \(t _{0}=0.01 t _{ T }=25 \times 10^{-14}\, m\) \(=25\)

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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