In the pulley system shown the movable pulleys `A,B` and `C` have mass m each, `D` and `E` are fixed pulleys. The strings are vertical light and inextensible Then
.

Options

A. the tension throughout the string is the same and equals `T =(2mg)/(3)` .
B. pulleys `A` and `B` have acceleration `(g)/(3)` each in downward direaction and pulley `C` has acceleration `(g)/(3)` in wpward direaction .
C. pulleys `A,B` and `C` all have accleration `(g)/(3)` in downward direction .
D. pulley `A` has acceleration `(g)/(3)` in downward direction and pulleys `B` and `C` have acceleration `(g)/(3)` each in upward direction .

Answer

A, B, D

Explanation

Let T be the tension in string.
`-2Ta_(C) + Ta_(B) - Ta_(A) = 0`

`a_(a) + 2a_(C) = a_(B)…..(i) , mg - 2T = ma_(C)`….(ii)
`T - mg = ma_(B)…..(ii) , mg-T = ma_(A)….(iv)`