Question

A cord is used to lower vertically a block of mass $M$ through distance $d$ at a constant downward acceleration of $\frac{g}{4}$. Then, the work done by the cord on the block is -

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

Answer 1

The correct option is D $-\frac{3Mgd}{4}$


From the FBD,

$Mg-F=Ma=\frac{Mg}{4}$

$\Rightarrow F=\frac{3Mg}{4}$

Therefore, the force applied by the cord is $\frac{3Mg}{4}$.

Since, displacement of the block is opposite to the force applied, the work done by the cord on the block is given by:

$W=-Fd$

$\Rightarrow W=-\frac{3Mg}{4}\times d$

$\Rightarrow W=-\frac{3Mgd}{4}$

Hence, option $\left(D\right)$ is the correct answer.