Question

If earth revolves around the sun in an orbit of double its present radius, then the year on earth will be of

• A. $\frac{365}{4}$day
• B. $365\times 2\sqrt{2}$day
• C. $\frac{365}{2\sqrt{2}}$day
• D. $365\times 4$day

Answer 1

Answer: (B)

$365\times 2\sqrt{2}$day

Using Kepler's law, $T^2\propto R^3$

Thus, $\frac{T_2^2}{T_1^2}=\frac{(2r{)}^3}{r^3}$

$⟹\frac{T_2}{T_1}=2\sqrt{2}$

Now as $T_1=365days$

Thus $T_2=365\times 2\sqrt{2}days$