એક કણને પૃથ્વીની સપાટીથી \(S\) ઊંચાઈએથી છોડવામાં આવે છે. કોઈ ચોક્કસ ઊંચાઈએ તેની ગતિઊ તેની સ્થિતિઊર્જા કરતાં ત્રણ ગણી વધારે છે. આ ક્ષણે કણની પૃથ્વીની સપાટીથી ઊંચાઈ અને ઝડપ અનુક્રમે \(.....\) છે.

A \(\frac{\mathrm{S}}{4}, \frac{3 \mathrm{gS}}{2}\)
B \(\frac{\mathrm{S}}{4}, \frac{\sqrt{3 g S}}{2}\)
C \(\frac{\mathrm{S}}{2}, \frac{\sqrt{3 \mathrm{gS}}}{2}\)
D \(\frac{\mathrm{S}}{4}, \sqrt{\frac{3 \mathrm{gS}}{2}}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\mathrm{S}}{4}, \sqrt{\frac{3 \mathrm{gS}}{2}}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{PE}+\mathrm{KE}=\mathrm{mgs}\) at given point

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 NEET

Explore more questions on app