A cord is used to lower vertically a block of mass M by a distance d with constant downward acceleration $\frac{\mathrm{g}}{4}$. Work done by the cord on the block is

When the block moves vertically downward with acceleration $\frac{\mathrm{g}}{4}$ then tension in the cord

$\mathrm{T}=\mathrm{M}\left(\mathrm{g}-\frac{\mathrm{g}}{4}\right)=\frac{3}{4}\mathrm{Mg}$

Work done by the cord = $\overrightarrow{\mathrm{F}}.\overrightarrow{\mathrm{s}}=\mathrm{Fscos\theta }$

$=\mathrm{Tdcos}(180°)=-\left(\frac{3\mathrm{Mg}}{4}\right)\times \mathrm{d}=-\frac{3}{4}\mathrm{Mgd}$