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: Understanding the Concept
Gravity provides the centripetal force: \(\dfrac{GMm}{r^2} = \dfrac{mv^2}{r}\), so \(v = \sqrt{\dfrac{GM}{r}}\).

Step 2: Take the ratio
\[ \frac{v_A}{v_B} = \sqrt{\frac{r_B}{r_A}} = \sqrt{100} = 10 \]
The nearer planet moves faster. Option (A) and (B) involve \(\sqrt{10}\), which would apply if \(r_B = 10 r_A\).

Final Answer:
The ratio is 10, option (C). \[ \boxed{10} \]