The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

Solution

Physics sir · 3 steps

Kepler's third law does the work: a quarter of the radius means one eighth of the period.

1. Kepler's third law. For any satellite of the same planet, the square of the period is proportional to the cube of the orbital radius. The mass of the satellite does not matter.

   T₂/T₁ = (r₂/r₁)^(3/2)

2. Put in numbers. Here r₂/r₁ = 1/4, so (1/4)^(3/2) = 1/(√4)³ = 1/2³ = 1/8. Then T₂ = (24 h)/8.
3. So. The new time period is T₂ = 3 h, which is option (b).

The idea to keep. For satellites of the same planet, use T² ∝ r³. Take the ratio of radii and raise it to the power 3/2. The period is not directly proportional to r.

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