A clock has second and minute hands of lengths 7.5 cm and 6.0 cm respectively. What is the ratio of the distance covered by the tip of the minute hand in 30 minutes to that covered by the tip of the second hand in 30 minutes?

Step 1: Identify the given information and the goal. Given: • Length of second hand, r_s = 75 cm • Length of minute hand, r_m = 60 cm • Time duration, T = 30 minutes • Value of = 3.14 Goal: Find the difference x in the distance traveled by the tip of the second hand and the tip of the minute hand in meters. x = Distance_second hand - Distance_minute hand Step 2: Convert the time duration to seconds. T = 30 minutes × 60 seconds/minute = 1800 seconds Step 3: Calculate the angular speed of each hand. The angular speed () is given by = (2)/(Period). • For the second hand: It completes one full revolution (2 radians) in 60 seconds. _s = 2 rad60 s = ()/(30) rad/s • For the minute hand: It completes one full revolution (2 radians) in 60 minutes. _m = 2 rad60 min = 2 rad3600 s = ()/(1800) rad/s Step 4: Calculate the angle rotated by each hand in T = 1800 seconds. The angle rotated () is given by = T. • For the second hand: _s = _s T = (()/(30) rad/s) × (1800 s) = 60 rad • For the minute hand: _m = _m T = (()/(1800) rad/s) × (1800 s) = rad Step 5: Calculate the distance traveled by the tip of each hand. The distance traveled (arc length, L) is given by L = r. • For the second hand: L_s = r_s _s = (75 cm) × (60 rad) = 4500 cm • For the minute hand: L_m = r_m _m = (60 cm) × ( rad) = 60 cm Step 6: Calculate the difference x and convert it to meters. x = L_s - L_m = 4500 cm - 60 cm x = (4500 - 60) cm = 4440 cm Substitute = 3.14: x = 4440 × 3.14 cm = 13941.6 cm Convert centimeters to meters (1 m = 100 cm): x = (13941.6)/(100) m = 139.416 m The approximate value of x is 139.4 m. The final answer is 139.4 m.