MHT CET · Physics · Gravitation
The period of revolution of planet A around the sun is 8 times that of planet B. How many times the distance of A from the sun is greater than that of B from the sun?
- A 5 times
- B 2 times
- C 3 times
- D 6 times
Answer & Solution
Correct Answer
(C) 3 times
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \left(\frac{\mathrm{R}_1}{\mathrm{R}_2}\right)^3=\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^2=(8)^2=64 \\ & \therefore \frac{\mathrm{R}_1}{\mathrm{R}_2}=(64)^{\frac{1}{3}}=4 \\ & \therefore \mathrm{R}_1=4 \mathrm{R}_2 \\ & \therefore \mathrm{R}_1-\mathrm{R}_2=4 \mathrm{R}_2-\mathrm{R}_2=3 \mathrm{R}_2\end{aligned}\)
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