This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
To solve this problem, we will use Newton's Law of Universal Gravitation. Given: • Mass of the planet = M_p • Mass of moon one = m • Mass of moon two = m (since they have equal mass) • Radius of orbit for moon one = r_1 = r • Radius of orbit for moon two = r_2 = 2r The formula for the gravitational force F between two objects with masses M and m separated by a distance R is: F = (GMm)/(R^2) where G is the gravitational constant. Step 1: Calculate the gravitational force on moon one (F_1). For moon one, the masses are M_p and m, and the distance is r. F_1 = (G M_p m)/(r^2) Step 2: Calculate the gravitational force on moon two (F_2). For moon two, the masses are M_p and m, and the distance is 2r. F_2 = (G M_p m)/((2r)^2) F_2 = (G M_p m)/(4r^2) Step 3: Compare F_2 with F_1. We can rewrite F_2 by factoring out (1)/(4): F_2 = (1)/(4) ((G M_p m)/(r^2)) Since F_1 = (G M_p m)/(r^2), we can substitute F_1 into the equation for F_2: F_2 = (1)/(4) F_1 This means the gravitational force on moon two is one fourth as large as the gravitational force on moon one. Step 4: Select the correct option. The result matches option D. The final answer is D) one fourth as large as that on moon one. 3 done, 2 left today. You're making progress.