If a planet has a radius 20% greater than that of the Earth but has the same mass as the Earth, what is the acceleration due to gravity at its surface?Select one:a.8.2 m/s2b.6.8 m/s2c.12 m/s2d.14 m/s2
Question
If a planet has a radius 20% greater than that of the Earth but has the same mass as the Earth, what is the acceleration due to gravity at its surface?Select one:a.8.2 m/s2b.6.8 m/s2c.12 m/s2d.14 m/s2
Solution
The acceleration due to gravity on the surface of a planet 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.
If the planet has the same mass as Earth, M is the same for both. If the radius of the planet is 20% greater than that of Earth, then r for the planet is 1.2r (where r is the radius of the Earth).
So, the acceleration due to gravity on the surface of the planet is:
g' = GM/(1.2r)^2 = GM/(1.44r^2) = g/1.44
The acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s^2. So, the acceleration due to gravity on the surface of the planet is:
g' = 9.8 m/s^2 / 1.44 ≈ 6.8 m/s^2
So, the correct answer is b. 6.8 m/s^2.
Similar Questions
What would be the acceleration (m/s2) due to gravity on a planet whose mass is 1/7th the mass of the earth and radius half the radius of the earth (g = 9.8 m/s2)a.4.2b.5.6c.3.4d.4.9
What is the acceleration due to gravity on Earth?Select one:a.10 m/s² downwardsb.9.8 m/s² downwardsc.10 m/s² upwardsd.9.8 m/s² upwards
Gravitational acceleration near the Earth’s surface is 9.8 m/s2 or 32.2 ft/s2. Which is greater, an acceleration of 1 m/s2or 1 ft/s2?Group of answer choices1 m/s21 ft/s2neither, they are equal quantitiesanswer cannot be determined from the information given
The acceleration due to gravity at the surface of Planet X is 10 m/s2. What is the acceleration due to gravity at an altitude of 4000 km above the surface of this planet?Select one:a.More information is needed.b.8.0 m/s2c.4.4 m/s2d.10 m/s2
What will be the value of acceleration due to gravity on the surface of the earth if the radius of the earth suddenly decreases to 60% of its present value, keeping the mass of the earth unchanged?*1 point5.89 m/s^29.81 m/s^216.35 m/s^227.14 m/s^2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.