An astronaut drops a marble on the surface of the airless Planet Z-49 and observes that it takes 1.02 s for the marble to fall 2.00 m starting from rest.She also knows that the radius of Z-49 is 3.39 × 10⁶ m.From this information,what will she determine for the mass of Z-49? (G = 6.67 × 10^-11 N ∙ m²/kg²) A)3.30 × $10^{23}$ kg. B)6.62 × $10^{23}$ kg. C)4.62 × $10^{23}$ kg. D)8.09 × $10^{23}$ kg. E)9.95 × $10^{23}$ kg.

Question

Quizplus · Accepted Answer

The force of gravity acting on the falling marble is given by F = mg, where m is the mass of the planet and g is the acceleration due to gravity. Using the formula for the period of a satellite in circular orbit, we know that g = GM/r^2, where M is the mass of the planet, r is the radius of the planet, and G is the gravitational constant.

Thus, we have:

F = mg = (GM/r^2)m

Solving for M, we get:

M = (Fr^2)/Gm

Substituting the given values, we get:

M = [(2.00 kg)(3.39 × 10^16 m)^2]/[(6.67 × 10^-11 N ∙ m^2/kg^2)(1.02 s)^2]

M = 6.62 × 10^23 kg

Therefore, the answer is B.

An Astronaut Drops a Marble on the Surface of the Airless