Question

The acceleration due to gravity on the surface of a planet is three times as large as it is on the surface of Earth. The mass density of the planet is known to be twice that of Earth. What is the radius of this planet in terms of Earth’s radius?

a) 0.5 times Earth's radius
b) 1.5 times Earth's radius
c) 2 times Earth's radius
d) 3 times Earth's radius

Answer 1

The radius of the planet is 1.5 times Earth's radius.

Step-by-step explanation:

To find the radius of the planet in terms of Earth's radius, we need to understand the relationship between acceleration due to gravity and mass density. The acceleration due to gravity is directly proportional to the mass of the planet and inversely proportional to the square of the radius.

If the acceleration due to gravity on the new planet is three times as large as it is on Earth, this means the mass of the planet is three times the mass of Earth. Since the mass density of the planet is known to be twice that of Earth, we can conclude that the radius of the planet must be 1.5 times Earth's radius (option b).