Question

The distance of Neptune and Saturn from sun are nearly 10¹³ and 10¹² meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio

• A. $\sqrt { 10 }$
• B. $100$
• C. $10 \sqrt { 10 }$
• D. $1 / \sqrt { 10 }$

Answer 1

Answer: (C)

$10 \sqrt { 10 }$

Answer 2

Kepler’s third law $T ^ { 2 } \propto R ^ { 3 }$ ∴ $\frac { T _ { \text {Nepptune } } } { T _ { \text {Saturn } } } = \left( \frac { R _ { \text {Nepptume } } } { R _ { \text {Saturn } } } \right) ^ { 3 / 2 } = \left( \frac { 10 ^ { 13 } } { 10 ^ { 12 } } \right) ^ { 3 / 2 } = 10 \sqrt { 10 }$ .