Question

Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are \(r_A\) and \(r_B\) respectively. Also \(r_B = 225\,r_A\). If the orbital speed of the planet A is 'V' then the orbital speed of planet B will be

• A. \(\frac{V}{3}\)
• B. \(\frac{V}{5}\)
• C. \(\frac{V}{15}\)
• D. \(\sqrt{15}\,V\)

Hint:

Orbital speed around the sun is inversely proportional to the square root of the orbit radius.

Answer 1

The Correct Option is C

Step 1: Use Kepler's third law:
$T^2 \propto r^3$, so $T_B = T_A\times100^{3/2} = 1000\,T_A$.

Step 2: Speed from period:
$v = \frac{2\pi r}{T}$, so $\frac{v_A}{v_B} = \frac{r_A}{r_B}\cdot\frac{T_B}{T_A} = \frac{1}{100}\times1000 = 10$ (C).

Final Answer:
10. \[ \boxed{10} \]