\(0.3\, m\) કેન્દ્રલંબાઈના એક બહિર્ગોળ કાચથી \(20\, m\) ના અંતરે એક વસ્તુ મુકેલ છે. આ કાચ વસ્તુનું પ્રતિબિંબ રચે છે. જો આ વસ્તુ \(5 \,m/s\) ની ઝડપ થી કાચથી દૂર તરફ ગતિ કરે, તો પ્રતિબિંબની ઝડપ અને દિશા ______ હશે.

A \(2.26\times 10^{-3}\,m/s\) કાચથી દૂર
B \(0.92\times 10^{-3}\,m/s\) કાચથી દૂર
C \(3.22\times 10^{-3}\,m/s\) કાચ તરફ
D \(1.16\times 10^{-3}\,m/s\) કાચ તરફ

Verified Solution

Answer & Solution

Correct Answer

(D) \(1.16\times 10^{-3}\,m/s\) કાચ તરફ

Step-by-step Solution

Detailed explanation

\(\frac{1}{V}-\frac{1}{-20}=\frac{1}{30}\) \( \Rightarrow \frac{1}{V} = \frac{1}{{0.30}} - \frac{1}{{20}} = \) \( + \frac{{200 - 3}}{{60}} = \frac{{197}}{{60}}\) \( \Rightarrow \quad - \frac{{dV}}{{dt\,\,{V^2}}} + \frac{{du}}{{dt\,{u^2}}} = 0\)…

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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