Three blocks of different masses connected with inextensible string are pulled by a force F on a frictionless surface as shown in the figure. The ratio of tensions T₁ to T₂ is

Step-by-step solution

Let the common acceleration of the system be a . Total mass of the system, M = 2 kg + 8 kg + 12 kg = 22 kg . The acceleration is given by a = F 22 . The tension T₁ is responsible for pulling the blocks of mass 2 kg and 8 kg together. Equation of motion for this combined mass is: T₁ = (2 + 8)a = 10a The tension T₂ is responsible for pulling only the block of mass 2 kg . Equation of motion for the 2 kg block is: T₂ = 2a The ratio of the tensions is: T₁ T₂ = 10a 2a = 5 1 Therefore, T₁ : T₂ = 5 : 1 . Answer: 5 : 1