Question

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :

• A. $\sqrt3$ years
• B. 3 years
• C. 9 years
• D. 3$\sqrt3$ years

Answer 1

Answer: (D)

3$\sqrt3$ years

Answer 2

We know that
$T^2 ∝ R^3$
$\Rightarrow$ $\bigg(\frac{T'}{T}\bigg)^2 = \bigg(\frac{3R}{R}\bigg)^3$

$\Rightarrow$ $\frac{T' }{ T} = 3\sqrt3$

$\Rightarrow$ $T' = 3\sqrt3$