Mechanics: motion of two equal masses connected by a light string over a smooth pulley One mass lies on a smooth horizontal plane; the other equal mass hangs freely over the pulley. Assume ideal (massless, inextensible) string and frictionless pulley; neglect air resistance. Decide whether the system will start moving with non-zero acceleration. Choose the correct statement.

Given data

• Two blocks of equal mass m connected by a light string over a smooth pulley.
• One block on a smooth horizontal table; the other hangs freely.

Concept/Approach

• Net external driving force on the system is the weight of the hanging block (m g). Total mass accelerated is 2m.

Step-by-step calculationResultant acceleration a = (driving force)/(total mass) = (m g)/(2m) = g/2.Tension T in the string equals m a = m g/2 (non-zero).

Verification/AlternativeEquations of motion: for the hanging block, m g − T = m a; for the horizontal block, T = m a. Adding gives m g = 2m a → a = g/2 ≠ 0.

Common pitfalls

• Equilibrium would occur only if opposing friction balanced m g, but the plane is smooth (no friction).

Final AnswerAgree — the system accelerates (a = g/2).