In the pulley system shown in figure the movable pulleys A, B and C are of mass 1 kg each. D and E are fixed pulleys. The strings are light and inextensible.

Choose the correct alternative (s).

In the figure

$\left({\mathrm{y}}_{\mathrm{B}}-{\mathrm{y}}_{\mathrm{A}}\right)+{\mathrm{y}}_{\mathrm{B}}+2{\mathrm{y}}_{\mathrm{A}}+\left({\mathrm{y}}_{\mathrm{C}}-{\mathrm{y}}_{\mathrm{B}}\right)+{\mathrm{y}}_{\mathrm{C}}=\text{ constant }$

Take the second derivative of this equation w.r.t. time to get

$\begin{array}{l}{\mathrm{a}}_{\mathrm{A}}+{\mathrm{a}}_{\mathrm{B}}+2{\mathrm{a}}_{\mathrm{C}}=0 .......\left(1\right)\\ \mathrm{T}+\mathrm{mg}-2\mathrm{T}={\mathrm{ma}}_{\mathrm{A}} .......\left(2\right)\\ \mathrm{T}+\mathrm{mg}-2\mathrm{T}={\mathrm{ma}}_{\mathrm{B}} ........\left(3\right)\\ \mathrm{mg}-2\mathrm{T}={\mathrm{ma}}_{\mathrm{C}} .......\left(4\right)\end{array}$

Substituting m = 1 and solving the four equations, we get ${\mathrm{a}}_{\mathrm{A}}={\mathrm{a}}_{\mathrm{B}}=-{\mathrm{a}}_{\mathrm{C}}=\frac{\mathrm{g}}{3}\text{ and }\mathrm{T}=6.5\mathrm{N}$