An astronaut drops a marble on the surface of Mars and observes that it takes 1.02 s for the marble to fall 2.00 m. She also knows that the radius of Mars is 3.39 × 10⁶ m and that G = 6.67 x 10^-11 N·m²/kg². From this information, she can conclude that the mass of Mars is A) 3.30 × 10²³ kg. B) 6.62 × 10²³ kg. C) 4.62 × 10²³ kg. D) 8.09 × 10²³ kg. E) 9.95 × 10²³ kg.

Question

Quizplus · Accepted Answer

Using the formula for gravitational acceleration $ g = \frac{2d}{t^2} $, we find $ g \approx 1.92 \, \text{m/s}^2 $. Then, using $ g = \frac{GM}{R^2} $, we solve for $ M $ and find $ M \approx 6.62 \times 10^{23} \, \text{kg} $.

An Astronaut Drops a Marble on the Surface of Mars