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 grav

examrobotsa's picture

Submitted by examrobotsa on

Q: 45 (NDA-II/2018)
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?

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,26,19,7,5,26,7

keywords: 

{'first planet': [0, 0, 0, 1], 'gravity': [0, 0, 0, 6], 'planet': [4, 0, 1, 1], 'acceleration': [0, 0, 2, 8], 'g1': [0, 0, 0, 1], 'radius': [0, 0, 2, 2], 'mass': [0, 0, 2, 3], 'mass m1': [0, 0, 0, 1], 'surface': [1, 0, 0, 0]}

The question states that planet 2 has a mass and radius that are both two times that of planet 1. We need to determine the acceleration due to gravity on the surface of planet 2.

The acceleration due to gravity is given by the formula g = GM/R^2, where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

Comparing planet 2 to planet 1, we see that the mass of planet 2 is 2 times the mass of planet 1, and the radius of planet 2 is also 2 times the radius of planet 1.

Plugging these values into the formula for acceleration due to gravity, we get g2 = (2G(2M1))/(2R1)^2 = (4GM1)/(4R1^2) = GM1/R1^2 = g1.

Therefore, the acceleration due to gravity on the surface of planet 2 is equal to the acceleration due to gravity on the surface of planet 1.

In terms of the options given, option 1 (g1) is incorrect because acceleration due to gravity on planet 2 is not equal to g1. Option 2 (2g1) is incorrect

Practice this on app