A bucket filled with water weighing 50kg is raised from a well of depth 100m.if the linear density of the rope is 1kg per metre.then the work done is?

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Answer 1 · 2018-04-04T09:29:05

#"198 kJ"#

Work is done to raise #"50 kg"# bucket and rope.

Work done to raise the bucket

#"W"_1 = "mgh = 50 kg × 9.8 m/s"^2 × "100 m" = 49 × 10^3\ "J"#

Length of the rope is equal to depth of the well. Mass of the rope is

#"m"_"rope" = 100 cancel"m" × "1 kg"/cancel"m" = "100 kg"#

Whole rope is not at the depth of #"100 m"#. So, let’s take work done to raise the centre of mass of rope. It is

#"W"_2 = "m"_"rope" "gh’" = "100 kg" × "9.8 m/s"^2 × "100 m"/2 = 49 × 10^3\ "J"#

Work done #"= W"_1 + "W"_2 = 2 xx 49 × 10^3\ "J" = "198 kJ"#