Question #20a23

1 Answer
Nov 6, 2016

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"#