Question

A body revolved around the sun 27 times faster then the earth what is the ratio of their radii

• A. 1/3
• B. 1/9
• C. 1/27
• D. ј

Answer 1

Answer: (B)

1/9

Answer 2

$\omega _ { \text {body } } = 27 \omega _ { \text {earth } }$

$T ^ { 2 } \propto r ^ { 3 } \Rightarrow \omega ^ { 2 } \propto \frac { 1 } { r ^ { 3 } } \Rightarrow \omega \propto \frac { 1 } { r ^ { 3 / 2 } }$∴$r \propto \frac { 1 } { \omega ^ { 2 / 3 } }$

⇒ $= \left( \frac { 1 } { 27 } \right) ^ { 2 / 3 } = \frac { 1 } { 9 }$