Question #20a23

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Answer 1 · 2016-11-06T15:37:48

Given

$h->"the depth of the well"=12m$

This will also be the length if the rope

$M->"the mass of bucket+ water in it"=15kg$

$W->"the work done to raise the bucket"$
$"filled with water"=2160J$

Let the mass of the rope be m kg

The total work done against the gravitional pull will be

$W=Mgh+mg*h/2$

Here $mg*h/2$ is the work done to raise the center of gravity ( at $h/2$ depth) of the rope.

So

$Mgh+mg*h/2=2160$

$=>15*9.8*12+m*9.8*12/2=2160$

$=>m=(2160-15*9.8*12)/(9.8xx6)=6.73kg$

So linear density of the rope

$="mass of the rope (m)"/"length of the rope (h)"$

$=6.73/12~~0.56" kg/m"$