'\(d\)' ઊંડાઈના પાત્રમાં અડધે સુધી \(n _1\) વક્રીભવનાંક ધરાવતું તેલ, અને બાકીનો અડધો ભાગ \(n _2\) વક્રીભવનાંક ધરાવતા પાણીથી ભરવામાં આવે છે.જ્યારે આા પાત્રમાં ઉપરથી જોતાં તેની દેખાતી ઊંડાઈ \(.........\) થશે.

A \(\frac{d n_1 n_2}{\left(n_1+n_2\right)}\)
B \(\frac{d\left(n_1+n_2\right)}{2 n_1 n_2}\)
C \(\frac{d n_1 n_2}{2\left(n_1+n_2\right)}\)
D \(\frac{2 d \left( n _1+ n _2\right)}{ n _1 n _2}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{d\left(n_1+n_2\right)}{2 n_1 n_2}\)

Step-by-step Solution

Detailed explanation

Formula used \(d _{ app }=\frac{ d _1}{ n _1}+\frac{ d _2}{ n _2}\) \(d _{a p p}=\frac{ d }{2}\left\lfloor\frac{ n _1+ n _2}{ n _1 n _2}\right\rfloor\)

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.

Same subject

Explore more questions on app

From JEE Mains

Explore more questions on app