Q. A bucket tied to a string is lowered at a constant acceleration of $\frac{g}{4}$. If the mass of the bucket is $m$ and is lowered by a distance $d$, the work done by the string will be
A) $\frac{mgd}{4}$
B) $- \frac{3}{4}mgd$
C) $- \frac{4}{3}mgd$
D) $\frac{4}{3}mgd$
Explanation
(b) From force diagram as shown in figure
$mg - T = ma$
[image:6_image57.emf]
$T = mg - ma = mg - \frac{mg}{4} = \frac{3mg}{4}$
$\therefore\ W_{T} =$ work done by tension
$= \overrightarrow{\mathbf{T}}.\overrightarrow{\mathbf{s}} = Ts\cos{180{^\circ}} = - \frac{3mgd}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.