Question

A bucket tied to a string is lowered at a constant acceleration of $g/4$. If the mass of the bucket is $m$ and is lowered by a distance $d$, the work done by the string on bucket will be:(assume the string to be massless, acceleration due to gravity $=g$)

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

Answer 1

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

Let tension in string be $T$, then work done by tension $=-Td$

Applying newton's second law on the bucket:

$mg-T=m\left(\frac{g}{4}\right)$ or $T=\frac{3}{4}mg$

$\therefore$ required work done $=-\frac{3}{4}mgd$