If the mass of Venus is 0.786 times that of Earth,and its radius is 0.950 that of Earth,estimate the gravitational acceleration g at the surface of Venus.(g_earth = 9.80 m/s²) A)7.31 m/s² B)3.73 m/s² C)8.27 m/s² D)8.53 m/s²

Question

Quizplus · Accepted Answer

We can use the formula for gravitational acceleration at the surface of a planet:
g = G * (M/R^2)

where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

Let's use subscript V and subscript E to denote Venus and Earth, respectively.

From the problem, we know that:
M_V = 0.786 * M_E
R_V = 0.950 * R_E

Substituting these values into the formula for g, we get:
g_V = G * (M_V/R_V^2)
= G * (0.786*M_E)/(0.950*R_E)^2
= G * 0.786/(0.950)^2 * (M_E/R_E^2)
= 0.813 * g_E

where g_E is the gravitational acceleration at the surface of Earth.

Substituting g_E = 9.80 m/s^2, we get:
g_V = 0.813 * 9.80 m/s^2
= 7.97 m/s^2

Therefore, the closest answer is D) 8.53 m/s^2.

If the Mass of Venus Is 0