A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution :

Solution

Physics sir · 3 steps

Kepler's third law: cut the distance to one fourth and the period drops by a factor of 4^(3/2) = 8.

1. Kepler's third law. For planets going round the same Sun, T² ∝ r³. So the ratio of two periods depends only on the ratio of the two distances.

   T₂/T₁ = (r₂/r₁)^(3/2)

2. Put in numbers. Here r₂/r₁ = 1/4, so (1/4)^(3/2) = 1/8. That gives T₂ = 200/8 days.
3. So. T₂ = 25 days, which is option (d).

The idea to keep. Whenever the same central body is involved, use T ∝ r^(3/2). Square root first, then cube, and the period ratio follows straight from the distance ratio.

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