Question

The distance of the two planets A and B from the sun are '\(r_A\)' and '\(r_B\)' respectively such that \(r_B = 100\,r_A\). The ratio of the speed of planet A to that of planet B is (both the planets are revolving around the sun)

• A. \(\frac{1}{\sqrt{10}}\)
• B. \(\sqrt{10}\)
• C. \(10\)
• D. \(10\sqrt{10}\)

Hint:

For a circular orbit, v = sqrt(GM/r), so v is inversely proportional to the square root of r.

Answer 1

The Correct Option is C

Step 1: Orbital speed
$v \propto r^{-1/2}$ for the same central mass.

Step 2: Substitute
$v_A/v_B = (r_B/r_A)^{1/2} = (100)^{1/2}$.

Step 3: Result
10. Option (C).

Final Answer:
Option (C). \[ \boxed{10} \]