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
Here's how to determine the accelerations for each system: Step 1: Analyze System A In System A, a mass m is attached to one end of a string, and a force F_1 = 2mg is applied to the other end. Assuming an ideal pulley and string, the tension T throughout the string is equal to the applied force. T = F_1 = 2mg For the mass m, the forces acting are its weight mg downwards and the tension T upwards. Applying Newton's second law (F_net = ma_1): T - mg = ma_1 2mg - mg = ma_1 mg = ma_1 a_1 = g Step 2: Analyze System B In System B, a mass m is on one side and a mass 2m is on the other side. This is an Atwood machine. Let T be the tension in the string and a_2 be the acceleration. We assume 2m moves down and m moves up. For mass m: T - mg = ma_2 (1) For mass 2m: 2mg - T = (2m)a_2 (2) Adding equations (1) and (2): (T - mg) + (2mg - T) = ma_2 + 2ma_2 mg = 3ma_2 a_2 = (mg)/(3m) a_2 = (g)/(3) Step 3: Analyze System C In System C, a mass m is on the left, and a mass m is on the right with an additional downward force F_2 = mg. Let T be the tension and a_3 be the acceleration. We assume the right side moves down and the left side moves up. For the left mass m: T - mg = ma_3 (1) For the right mass m, the total downward force is its weight mg plus the applied force F_2 = mg. So, the total downward force is mg + mg = 2mg. 2mg - T = ma_3 (2) Adding equations (1) and (2): (T - mg) + (2mg - T) = ma_3 + ma_3 mg = 2ma_3 a_3 = (mg)/(2m) a_3 = (g)/(2) Step 4: Compare the accelerations We have the accelerations: a_1 = g a_2 = (g)/(3) a_3 = (g)/(2) Comparing these values: g > (g)/(2) > (g)/(3) Therefore, a_1 > a_3 > a_2. This matches option (b). The final answer is (b).