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  4. A cord is used to lower vertically a block of mass m by a distance d with constant downward acceleration ( g /4) Work done by the cord on the block is

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Q. A cord is used to lower vertically a block of mass $m$ by a distance d with constant downward acceleration $\frac{ g }{4}$ Work done by the cord on the block is

Work, Energy and Power

Solution:

$T=m(g-a)$ (downward)
$T=m\left(g-\frac{g}{4}\right)=\frac{3mg}{4}$
$\therefore $ work done by the cord $=\vec{F} \cdot \vec{s} \cos \theta$
$=\frac{3mg}{4} \times d\, \cos 180^{\circ}$
$W=\frac{-3 mgd}{4} \,J$