WBJEE · Physics · Gravitation
Assume that the earth moves around the sun in a circular orbit of radius \(R\) and there exists a planet which also move around the sun in a circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is
- A \(2^{-2 / 3} R\)
- B \(2^{2 / 3} R\)
- C \( 2^{-1 / 3} R\)
- D \(\frac{R}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(2^{-2 / 3} R\)
Step-by-step Solution
Detailed explanation
According to the Kepler's third law \[ T^{2} \propto r^{3} \] where, \(T=\) time period of revolution \(r=\) radius Now, \(\left(\frac{T_{E}}{T_{P}}\right)^{2}=\left(\frac{r_{E}}{r_{P}}\right)^{3}=\frac{r_{E}}{r_{P}}=\left(\frac{T_{E}}{T_{P}}\right)^{2 / 3}\)…
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