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
Step 1: Calculate the angular speed of the second hand. The second hand completes one full revolution (2 radians) in 60 seconds. The time period for the second hand is T_s = 60 seconds. The angular speed _s is given by: _s = (2)/(T_s) = (2)/(60) rad/s Step 2: Calculate the angular speed of the hour hand. The hour hand completes one full revolution (2 radians) in 12 hours. First, convert 12 hours to seconds: T_h = 12 hours × 60 minutes/hour × 60 seconds/minute T_h = 12 × 3600 seconds = 43200 seconds The angular speed _h is given by: _h = (2)/(T_h) = (2)/(43200) rad/s Step 3: Calculate the ratio of the angular speed of the second hand to the angular speed of the hour hand. (_s)/(_h) = (2)/(60)(2)/(43200) (_s)/(_h) = (2)/(60) × (43200)/(2) (_s)/(_h) = (43200)/(60) (_s)/(_h) = (4320)/(6) (_s)/(_h) = 720 The ratio is 720:1. The final answer is (c) 720:1.