Physics
Physics
Problem
For a light, inextensible string passing over a smooth pulley and connecting two bodies, which one of the following statements is correct? a) The tension is equal to the difference between the weights of the two bodies. b) The tension is the same throughout the string on both sides of the pulley. c) The tension is equal to the weight of each body irrespective of their masses. d) The tension is greater on the side carrying the heavier body.Intuitive explanation
The key insight is that an ideal string over a smooth pulley transmits tension uniformly and forces both masses to accelerate together at the same rate. Rather than treating each mass separately, recognize that the constraint—the string length is fixed—couples their motions: if one accelerates down, the other accelerates up by the same amount. This shared acceleration is what makes the system solvable and determines which statements about tension, forces, or motion are physically consistent.
Intuitive explanation
The key insight is that an ideal string over a smooth pulley transmits tension uniformly and forces both masses to accelerate together at the same rate. Rather than treating each mass separately, recognize that the constraint—the string length is fixed—couples their motions: if one accelerates down, the other accelerates up by the same amount. This shared acceleration is what makes the system solvable and determines which statements about tension, forces, or motion are physically consistent.