\(4:3\) જેટલો દળનો ગુણોત્તર ધરાવતા બે ઉપગ્રહો \(A\) અને \(B\) અનુક્રમે \(3r\) અને \(4 r\) ત્રિજ્યાઓ ધરાવતા વર્તુળાકાર કક્ષાઓમાં ભ્રમણ કરે છે. \(A\) અને \(B\) ની કુલ યાંત્રિક ઊર્જાનો ગુણોત્તર ......... થશે.

A \(9: 16\)
B \(16: 9\)
C \(1: 1\)
D \(4: 3\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(16: 9\)

Step-by-step Solution

Detailed explanation

Given that \(\frac{m_{1}}{m_{2}}=\frac{4}{3}, \frac{r_{1}}{r_{2}}=\frac{3}{4}\) Now \(T E=\frac{1}{2} mv ^{2}+\left(\frac{- GMm }{ r }\right)\) but \(\frac{ mv ^{2}}{ r }=\frac{ GMm }{ r ^{2}} \Rightarrow mv ^{2}=\frac{ GMm }{ r }\)…

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

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

લીસ્ટ \(I\)	લીસ્ટ \(II\)
\(A\) પલાન્ક અચળાંક \(( h )\)	\(I\) \(\left[ M ^1 L ^2 T ^{-2}\right]\)
\(B\) સ્ટોપિંગ પોટેન્શિયલ \(( Vs )\)	\(II\) \(\left[ M ^1 L ^1 T ^{-1}\right]\)
\(C\) કાર્ય વિધેય \((\phi)\)	\(III\) \(\left[ M ^1 L ^2 T ^{-1}\right]\)
\(D\) વેગમાન \(( p )\)	\(IV\) \(\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]\)

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