Three frictionless pulleys with rope attachment are in a static equilibrium as shown in the figure. The mass \( m_1 \) and \( m_2 \), in kg, respectively are:
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In pulley systems in static equilibrium, remember that the forces acting on each mass must balance. The tensions in the ropes and the weights of the masses are key to solving such problems.
In this question, the system is in static equilibrium, which means the net forces acting on the system must sum to zero. Step 1: Analyze the forces on the system. The weight of the mass \( 100 \, {kg} \) creates a force acting downwards. For the system to be in equilibrium, the forces acting on the pulleys must balance. Let the tension in the rope be denoted as \( T \). Step 2: Set up the equilibrium equations. For the pulley system, the forces must satisfy the condition for static equilibrium. This leads to the following relationships between the masses: The tension force in the rope is the same at all points (since the pulleys are frictionless). The total force on the mass \( m_1 \) and \( m_2 \) must balance the downward force from the \( 100 \, {kg} \) mass. Using these relationships, we find that: \( m_1 = 50 \, {kg} \) \( m_2 = 100 \, {kg} \) Conclusion: The correct answer is (A) 50, 100.
