બે સમાન કાર \(A\) અને \(B\) ની ગતિ ઊર્જા અનુક્રમે 100 J અને 225 J છે. બ્રેક લગાવતા, કાર A 1000 m પછી અટકે છે અને કાર B 1500 m પછી અટકે છે. જો કાર A અને B પર બ્રેક દ્વારા લાગુ પડેલા બળો અનુક્રમે \(F _{ A }\) અને \(F _{ B }\) હોય, તો ગુણોત્તર \(F _{ A } / F _{ B }\) ....છે :

A \(\frac{3}{2}\)
B \(\frac{2}{3}\)
C \(\frac{1}{3}\)
D \(\frac{1}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2}{3}\)

Step-by-step Solution

Detailed explanation

\(\because \text {કાર્ય }=\Delta KE \)
\( \overrightarrow{ F } \cdot \overrightarrow{ S }=\Delta KE \)
\( \frac{(\Delta K E)_A}{(\Delta K E)_B}=\frac{- F _A S_A}{- F _{ B } S _{ B }} \)
\( \frac{-100}{-225}=\frac{- F _{ A }(1000)}{- F _{ B }(1500)} \)
\( \frac{ F _{ A }}{ F _{ B }}=\frac{2}{3}\)

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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