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PHY 101 PHY 101 Past Questions Objective Question
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Question

The mean diameters of Mars and Earth are 6.9 × 10³ km and 1.3 × 10⁴ km, respectively. What is the value of the gravitational acceleration on Mars and the escape speed on Mars? (Duplicate)
Options
A 3.8 m/s², 5.0 km/s
Correct Answer
B 8.3 m/s², 50 m/s
C 5 m/s², 38 m/s
D 6.9 m/s², 134 km/s
Correct Answer

Option A is the correct answer.

Detailed Explanation

Using Earth values g_E = 9.8 m/s², v_esc_E = 11.2 km/s. Mass ratio Mars/Earth ≈ 0.107, radius ratio = (6.9×10³)/(1.3×10⁴) = 0.531. Then g_M = g_E × (M_M/M_E) / (R_M/R_E)² = 9.8 × 0.107 / (0.531)² = 9.8 × 0.107 / 0.282 = 9.8 × 0.379 = 3.72 m/s² ≈ 3.8 m/s². v_esc_M = v_esc_E × √((M_M/M_E)/(R_M/R_E)) = 11.2 × √(0.107/0.531) = 11.2 × √0.2015 = 11.2 × 0.449 = 5.03 km/s ≈ 5.0 km/s.

Hint

Use ratios based on Earth's values: g ∝ M/R², v_esc ∝ √(M/R).

Question Info

Course: PHY 101
Topic: PHY 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 895 of 1250
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