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 × kg. B)6.62 × kg. C)4.62 × kg. D)8.09 × kg. E)9.95 × kg.

Question

Quizplus · Accepted Answer

Using the equation for the acceleration due to gravity,

g = GM/r^2

where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet, we can solve for M:

M = gr^2/G

Using the given values, 
g = 2.00 m / (1.02 s)^2 = 1.942 m/s^2 
r = 3.39 × 10^16 m

Plugging in these values for g, r, and G, we get:

M = (1.942 m/s^2) x (3.39 × 10^16 m)^2 / (6.67 × 10^-11 N*m^2/kg^2) = 6.62 x 10^11 kg

Therefore, the answer is B: 6.62 × 10^11 kg.

An Astronaut Drops a Marble on the Surface of the Airless