धनात्मक \(x\)-दिशा में संचरित किसी तरंग विक्षोभ का आयाम समय \(t =0\) पर \(y =\frac{1}{(1+ x )^{2}}\) द्वारा तथा \(t =\) 1s पर \(y =\frac{1}{1+( x -2)^{2}}\) द्वारा दर्शाया गया है, यहाँ \(x\) और \(y\) मीटर में हैं। संचरण के समय तरंग की आकति में परिवर्तन नहीं होता है। तरंग का वेग \(\dots\;m / s\) होगा।

A \(2\)
B \(4\)
C \(6\)
D \(8\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(2\)

Step-by-step Solution

Detailed explanation

At \({t}=0, {Y}=\frac{1}{1+{x}^{2}}\) \(\text { At time } t=t, y=\frac{1}{1+(x-v t)^{2}}\) \(\text { At } t=1, y=\frac{1}{1+(x-v)^{2}}....(i)\) \(\text { At } t=1, y=\frac{1}{1+(x-2)^{2}}....(ii)\) comparing \((i) \& (ii)\)

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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From JEE Mains

सूची-I को सूची-II से सुमेलित कीजिए।

	सूची-I		सूची-II
A.	श्यानता गुणांक	I.	\(\left[ ML ^{-1} T^{-2}\right]\)
B.	पृष्ठ तनाव	II.	\(\left[ ML ^2 T^{-2}\right]\)
C.	दाब	III.	\(\left[ ML ^0 T^{-2}\right]\)
D.	पृष्ठ ऊर्जा	IV.	\(\left[ ML ^{-1} T^{-1}\right]\)

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