એક કણ અચળ પ્રવેગ \(a\) થી ગતિ કરે છે. તેનો \(v^{2}\) વિરુદ્ધ \(x\) (સ્થાનાંતર) નો ગ્રાફ આપેલ છે. કણનો પ્રવેગ (\({m} / {s}^{2}\) માં) કેટલો હશે?

A \(100\)
B \(20\)
C \(14\)
D \(1\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(1\)

Step-by-step Solution

Detailed explanation

\({y}={m} {x}+{C}\) \({v}^{2}=\frac{20}{10} {x}+20\) \({v}^{2}=2 {x}+20\) \(2 {v} \frac{{d} {v}}{{d} {x}}=2\) \(\therefore {a}={v} \frac{{d} {v}}{{d} {x}}=1\)

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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લીસ્ટ \(I\) સાથે લીસ્ટ \(II\) યોગ્ય રીતે જોડો.

લીસ્ટ \(-I\)	લીસ્ટ \(-II\)
\((A)\) ટોર્ક	\((I)\) \(kg\,m ^{-1}\,s ^{-2}\)
\((B)\) ઉર્જા-ઘનતા	\((II)\) \(kg\,m\,s^{-1}\)
\((C)\) દબાણ પ્રચલન	\((III)\) \(kg\,m ^{-2}\,s ^{-2}\)
\((D)\) આઘાત	\((IV)\) \(kg\,m ^2\,s ^{-2}\)

નીચે આપેલ વિકલ્પોમાંથી સાચો ઉત્તર પસંદ કરો.

JEE Mains 2023 Medium

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