Question

Three identical blocks, of mass M each, are connected to each other by inextensible strings and are kept on a smooth horizontal floor. On applying a force F, as shown, the system moves with an acceleration a. If the tensions in the two strings are T₁ and T₂ , respectively, the ratios (F/T₂) and (F/T₁) equal respectively to

(1) 3 and 1.5

(2) 1.5 and 3

(3) 2 and 1

(4) 1 and 2

Answer 1

(2) 1.5 and 3

For the first mass, on the right, we have

F - T = Ma

For the second mass, we have

T₂ - T₁ = Ma

For the third mass, we have

T₁ = Ma

Adding the three equations, we get

F = 3Ma or a = F/3M

∴ F - T₂ = M.F/3M = F/3

∴ T₂ = 2F/3

Also, T₁ = Ma = M.F/3M = F/3

∴ F/T₂ = 3/2 = 1.5

and F/T₁ = 3