Question

A cord is used to lower vertically a block of mass M by a distance d with constant downward acceleration Work done by the cord on the block is

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

Answer 1

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

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