Question

A cord is used to raise a block of mass $m$ vertically through a distance $d$ at a constant downward acceleration $g/4$. The work done by the cord is:

• A. $mgd/4$
• B. $3Mgd/4$
• C. $-3Mgd/4$
• D. $Mgd$

Answer 1

The correct option is B $3Mgd/4$

Acceleration due to gravity $=g$ (downwards)
Since the block is moving up at a constant downward acceleration $\left(g/4\right)$, this implies the cord exerts an external force on the block in upward direction.
Upward acceleration given to the block by the cord $=g-\frac{g}{4}=\frac{3g}{4}$ (upwards)
Work done by the cord $W=F_{cord}d=M\frac{3g}{4}d$