Question

The period of revolution of the planet A around the sun is 27 times that of another planet B. If the distance of A from the sun is \( X \) times greater than that of B from the sun, then the value of \( X \) is

• A. \(8 \)
• B. \(4 \)
• C. \(9 \)
• D. \(3 \)
• E. \(12 \)

Hint:

For orbital motion, always use \( T^2 \propto r^3 \).

Answer 1

The Correct Option is C

Concept: Kepler’s third law: \[ T^2 \propto r^3 \]

Step 1: Apply relation.
\[ \left(\frac{T_A}{T_B}\right)^2 = \left(\frac{r_A}{r_B}\right)^3 \] \[ 27^2 = X^3 \Rightarrow 729 = X^3 \]

Step 2: Solve.
\[ X = 9 \]