A light rope is passed over a pulley such that at its one end a block is attached , and on the other end a boy is climbing up with acceleration `g/2` relative to rope. Mass of the block is 30 kg and that of the boy is 40 kg. Find the tension and acceleration of the rope .

Explanation

Let's assume tension in rope is T. Acceleration of block is `a_(1)` and that of boy is `a_(2)` . As string is inextensible so the acceleration of point B will be `(-a_(1))`
The acceleration of boy w.r.t. rope ` = a_(2) - a_(B)`
`g/2 = a_(2) + a_(1) " " ` ....(i)
Now applying Newton's 2nd law for the block and the boy
` T - 30 g = 30 a_(1) " "`(ii)
` T - 40 g = 40 a_(2) " " `....(iii)
Solving equation (i), (ii) and (iii)
` T = (300g)/7 and a_(1) = (3g)/7` (upward)