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

Solution

Physics sir · 3 steps

Kepler's third law says T² ∝ R³, so tripling the distance multiplies the year by 3^(3/2).

1. Kepler's third law. For a planet going round the Sun, the square of the time period is proportional to the cube of the orbit radius. The Sun's mass sets the constant, and it stays the same here.

   T₂/T₁ = (R₂/R₁)^(3/2)

2. Put in numbers. T₁ = 1 year and R₂/R₁ = 3. So T₂ = 3^(3/2) = 3 × √3 years, which is about 5.2 years.
3. So. The new year lasts 3√3 years, option (d).

The idea to keep. For orbits around the same central body, T ∝ R^(3/2). Take the radius ratio, raise it to the power 3/2, and you have the period ratio.

Answer from the NTA final answer key. Solution by PrepWiser.