StemCET Logo

Physics Question 30 – JEE-MAIN 2026

← Back
A planet (P1) is moving around the star of mass 2M in the orbit of radius R. Another planet (P2) is moving around another star of mass 4M in a orbit of radius 2R. Ratio of time periods of revolution of P2 and P1 is _______.

Recall the relationship between orbital period, orbital radius, and the mass of the central body for a planet in a circular orbit.

Step 1: Apply Kepler's Third Law for each planet✦ Active

Kepler's Third Law states that T2=KR3M, where K=4π2G is a constant. Let's apply this for both planets:

T12=KR13M1=KR32M
T22=KR23M2=K(2R)34M=K8R34M=K2R3M
Step 2: Calculate the ratio of the squares of the time periods○ Expand

Now, we find the ratio of T22 to T12:

T22T12=K2R3MKR32M=21/2=4
Step 3: Find the ratio of the time periods○ Expand

To get the ratio of the time periods, we take the square root of the ratio of their squares:

T2T1=4=2
💡 Teacher's Secret Hint

Ensure to take the square root at the final step to get the ratio of periods, not the ratio of periods squared.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.