If a planet has a radius 16.0% greater than that of the Earth but has the same mass as the Earth,what is the acceleration due to gravity at its surface? A)8.45 m/s² B)1.57 m/s² C)10.0 m/s² D)7.28 m/s²

Question

Quizplus · Accepted Answer

The formula for the acceleration due to gravity at the surface of a planet is given by g = (GM)/r^2, where G is the gravitational constant, M is the mass of the planet, and r is its radius. Since the planet has the same mass as Earth, we can use the value of G and the radius ratio to find the acceleration due to gravity as follows:

g' = (GM)/(1.16r)^2
g' = (GME)/(1.16r)^2
g' = (gE)(1.00)/(1.16)^2
g' = 0.862gE

where gE is the acceleration due to gravity on Earth. Plugging in the value of gE = 9.81 m/s^2, we get:

g' = 0.862(9.81) ≈ 8.45 m/s^2

Therefore, the answer is D) 7.28 m/s^2.

If a Planet Has a Radius 16