Three blocks are connected by massless cords and hung by a third massless cord to a beam.Mass m₁ = 2 m₂ = 3 m₃.Mass m₁ is the lowest block and m₃ is the highest.The tension in the cord between the two highest blocks is A)3m₁ $\times$ g/2 B)m₁ $\times$ g/2 C)m₁ $\times$ g/6 D)2m₁ $\times$ g/3 E)6m₁ $\times$ g/11

Question

Quizplus · Accepted Answer

Since the blocks are in equilibrium, the sum of the forces in the vertical direction must be zero. Let T1 be the tension in the cord between m₂ and m₃, and T2 be the tension in the cord between m₁ and m₂. The forces acting on m₃ are the force of gravity (mg) and the tension in the cord (T1). The forces acting on m₂ are the force of gravity (2mg) and the tensions in the cords (T1 and T2). The forces acting on m₁ are the force of gravity (3mg) and the tension in the cord (T2). Setting the sum of the forces equal to zero for each block, we get: m₃*g - T1 = 0 2m₂*g - T1 - T2 = 0 3m₁*g - T2 = 0 Solving for T1 and T2, we find: T1 = 3m₁*g/2 T2 = 2m₁*g/3 Therefore, the tension in the cord between the two highest blocks (T1) is 3m₁*g/2. The answer is (A).

Three Blocks Are Connected by Massless Cords and Hung by a Third