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

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Q: 60 (NDA-I/2019)
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

question_subject: 

Geography

question_exam: 

NDA-I

stats: 

0,2,11,2,7,4,0

The correct answer is option 1: g1 > g2.

The acceleration due to gravity on the surface of a planet is directly proportional to the mass of the planet and inversely proportional to the square of the radius. The equation that relates these quantities is:

g = GM/R^2

Where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

Since the two planets have the same density, it means that their masses are directly proportional to their volumes. The volume of a sphere is given by the equation:

V = (4/3)πR^3

Since the radius of planet 1 (R1) is greater than the radius of planet 2 (R2), it means that the volume and mass of planet 1 will be greater than that of planet 2.

As a result, when the mass and radius are plugged into the equation for gravity, the acceleration due to gravity on planet 1 (g1) will be greater than the acceleration due to gravity on planet 2 (g2).

Therefore, option 1 is the correct answer.