Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth.With g representing,as usual,the free-fall acceleration at the surface of Earth,the free-fall acceleration at the surface of Z-34 is
A)g/3.
B)3g.
C)6g.
D)g/9.
E)9g.

Question

Quizplus · Accepted Answer

The equation for free-fall acceleration (g) at the surface of a planet is given by:

g = (G*M) / R^2

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

For planet Z-34, we know that its mass is one-third that of Earth (M_Z-34 = (1/3)*M_Earth) and its radius is also one-third that of Earth (R_Z-34 = (1/3)*R_Earth).

Substituting these values into the equation for g, we get:

g_Z-34 = (G*((1/3)*M_Earth)) / ((1/3)*R_Earth)^2

g_Z-34 = (G*(1/3)*M_Earth) / ((1/9)*R_Earth^2)

g_Z-34 = (1/3)*(G*M_Earth) / R_Earth^2

g_Z-34 = (1/3)*g_Earth

Therefore, the free-fall acceleration at the surface of Z-34 is one-third that of Earth's (g_Z-34 = (1/3)*g_Earth) which means it is three times larger than Earth's (3g_Earth). Hence, the best choice is B.

Planet Z-34 Has a Mass Equal to One-Third That of Earth