Q: A block of mass ‘m’ is lowered with the help of a rope of negligible mass through a distance ‘d’ with an acceleration of g/3. Find the work done by the rope on the block?

Sol: During lowering a block,

m g – T = m a

Tension in rope is

T = m(g – a) and S = d

Work done , W = T S cos180°

W = – m (g – a)d

$\displaystyle W = – m (g – \frac{g}{3}) d $

$\displaystyle W = – \frac{2 m g d}{3}$