Question

The earth revolves around the sun in one year. If distance between them becomes double, the new time period of revolution will be:

• A. $4\sqrt{2}$ years
• B. $2\sqrt{2}$ years
• C. $4$ years
• D. $8$ years

Answer 1

The correct option is B $2\sqrt{2}$ years

According to Kepler's law.

$T^2\propto R^3$

$\because \frac{T_1^2}{T_2^2}=\frac{R_1^3}{R_2^2}$

$\Rightarrow \frac{I^2}{T_2^2}=\frac{R_1^3}{(2R_1{)}^3}=\frac{1}{8}$

$\Rightarrow T_2^2=8$

$\Rightarrow T_2=2\sqrt{2}$ years