An animation of four planets orbiting around the sun is shown below. Based on this animation, which of the following statement(s) is/are \textbf{TRUE? \quad [This question contains an animated GIF image.]}
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Count complete revolutions over equal time intervals. Convert the observed Blue-Green, Blue-Brown, and Red-Green comparisons to one common ratio before checking statement D.
When Planet Blue completes 2 orbits, Planet Green will complete 1 orbit.
When Planet Blue completes 3 orbits, Planet Brown will complete 2 orbits.
When Planet Green completes 1 orbit, Planet Red will complete 2 orbits.
When Planet Red completes 4 orbits, Planet Brown will complete 2 orbits.
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The Correct Option isA, B, C
Approach Solution - 1
Step 1: From the animation, observe that planets closer to the sun complete orbits faster, while those farther away take longer, consistent with relative angular speeds shown.
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Step 2: Compare orbital speeds by tracking how many times each planet completes a full revolution over the same time interval.
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Step 3:
\begin{itemize}
\item Statement A: Blue completes two orbits in the same time Green completes one — True.
\item Statement B: Blue completes three orbits while Brown completes two — True.
\item Statement C: Red completes two orbits in the time Green completes one — True.
\item Statement D: Brown completes fewer than two orbits when Red completes four — False.
\end{itemize}
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Final Answer:
\[
\boxed{\text{A, B and C}}
\]
\bigskip
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Approach Solution -2
Concept:
Compare the numbers of complete revolutions made by two planets during the same time interval.
Orbit-count ratios can be scaled without changing the relative motion.
Step 1: Record the Blue, Green, and Brown ratios from the animation.
Blue completes $2$ revolutions while Green completes $1$, so statement A is true. Blue completes $3$ while Brown completes $2$, so statement B is true.
Step 2: Compare Red with Green.
Red completes $2$ revolutions during one Green revolution. Therefore, statement C is true.
Step 3: Put all rates on one common scale.
Using $6$ Blue revolutions as a common interval gives Blue, Green, Brown, and Red counts in the ratio $6:3:4:6$. Thus Red and Brown are in the ratio $6:4=3:2$.
Step 4: Test statement D.
If Red completes $4$ revolutions, Brown completes $4\times\dfrac{2}{3}=\dfrac{8}{3}$ revolutions, not $2$. Hence statement D is false.
Final Answer: Statements A, B, and C are true.
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