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
Fresh day بنت, let's solve. Here's how to find the tension in the rope: Step 1: Convert the angular speed from revolutions per minute (rev/min) to radians per second (rad/s). Given angular speed = 120 rev/min We know that 1 revolution = 2π radians and 1 minute = 60 seconds. Angular speed (ω) = 120 (rev)/(min) × (2π rad)/(1 rev) × (1 min)/(60 s) ω = (120 × 2π)/(60) rad/s ω = 2 × 2π rad/s ω = 4π rad/s Step 2: Calculate the centripetal force. The tension in the rope provides the centripetal force (F_c). The formula for centripetal force using angular speed is: F_c = mω²r Where: m = mass of the object = 2 kg ω = angular speed = 4π rad/s r = radius of the circular path (length of the rope) = 1.2 m Step 3: Substitute the values into the formula and calculate the tension. Tension (T) = (2 kg) × (4π rad/s)² × (1.2 m) T = 2 × (16π²) × 1.2 N T = 32π² × 1.2 N T = 38.4π² N Using the approximate value of π ≈ 3.14159: π² ≈ (3.14159)² ≈ 9.8696 T = 38.4 × 9.8696 N T ≈ 378.99 N Rounding to the nearest whole number, the tension is approximately 379 N. Comparing this to the given options: A. 400 B. 288 C. 240 D. 379 The calculated tension matches option D. The tension in the rope is 379 N. D. 379 Send me the next one 📸