Question

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

• A. $M g \frac{d}{4}$
• B. $3 M g \frac{d}{4}$
• C. $-3 M g \frac{d}{4}$
• D. $Mgd$

Answer 1

Answer: (C)

$-3 M g \frac{d}{4}$

Answer 2

When the block moves vertically downward with acceleration $\frac{g}{4}$ then tension in the cord $T=M\left(g-\frac{g}{4}\right)=\frac{3}{4} M g$ Work done by the cord $=F \cdot s=F s \cos \theta$ $=T d \cos 180^{\circ}$ $=\left(-\frac{3}{4} M g\right) \times d$ $=-3 M g \frac{d}{4}$