Question

A bucket of mass $m$ tied to a light rope is lowered at a constant acceleration of $\frac{g}{4}$. If the bucket is lowered by a distance $d$, the work done by the rope will be (neglect the mass of the rope):

• A. $\frac{1}{4}mgd$
• B. $\frac{3}{4}mgd$
• C. $-\frac{3}{4}mgd$
• D. $-\frac{5}{4}mgd$

Answer 1

The correct option is C $-\frac{3}{4}mgd$

1) $2as=v^2-u^2$
$\Rightarrow 2\times \frac{g}{4}\times d=v^2$

$\Rightarrow v=\sqrt{\frac{gd}{2}}$
2) W.D (rope) + W.D ( gravity ) $=\Delta K.E$
W.D ( rope ) $=-mgd+\frac{1}{2}m\frac{gd}{2}$ $=\frac{-3}{4}mgd$