Change set

Pick exam & year, then Go.

Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading…
Q78 (NDA-II/2020) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Astronomy and astrophysics

Two planets orbit the Sun in circular orbits, with their radius of orbit as R1= R and R2 = 4R. Ratio of their periods (T1/T2) around the Sun will be

Result
Your answer: —  ·  Correct: B
Explanation

According to Kepler's Third Law of planetary motion, the square of the orbital period (T) of a planet is directly proportional to the cube of its orbital radius (R), expressed as T² ∝ R³ [1]. For two planets orbiting the same star, the ratio of their periods is given by (T1/T2)² = (R1/R2)³. Given the radii R1 = R and R2 = 4R, the ratio of the radii is R1/R2 = 1/4. Substituting this into the formula yields (T1/T2)² = (1/4)³, which simplifies to (T1/T2)² = 1/64. Taking the square root of both sides, we find the ratio of their periods T1/T2 = √(1/64) = 1/8. This law applies to all bodies in circular or elliptical orbits under the influence of gravity [2].

Sources

  1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 2: The Solar System > Kepler's Laws of Planetary Motion > p. 21
  2. [2] https://pwg.gsfc.nasa.gov/stargaze/Kep3laws.htm
How others answered
Each bar shows the % of students who chose that option. Green bar = correct answer, blue outline = your choice.
Community Performance
Out of everyone who attempted this question.
25%
got it right
✓ Thank you! We'll review this.

SIMILAR QUESTIONS

NDA-I · 2019 · Q60 Relevance score: 2.93

Suppose there are two planets, 1 and 2, having the same density but their radii are R1 and R2 respectively, where R1 > R 2. The accelerations due to gravity on the surface of these planets are related as

NDA-II · 2018 · Q45 Relevance score: 0.67

A planet has a mass M1 and radius R 1. The value of acceleration due to gravity on its surface is g 1. There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?

NDA-I · 2009 · Q24 Relevance score: 0.65

Assertion (A) : Two artificial satellites having different masses and revolving around the Earth in the same circular orbit have same speed. Reason (R) : The speed of a satellite is directly proportional to the radius of its orbit.

NDA-II · 2024 · Q95 Relevance score: 0.15

The masses of two planets are in the ratio of 1: 7. The ratio between their diameters is 2 : 1. The ratio of forces which they exert on each other is

IAS · 2006 · Q64 Relevance score: -0.05

Assertion (A) : To orbit around the Sun, the planet Mars takes lesser time than the time taken by the Earth. Reason (R) : The diameter of the planet Mars is less than that of the Earth.