Question

Question #20a23

Answer 1

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"`