Question

. A bucket filled with water weighing 20 kg is
raised from a well of depth 20m. If the linear
density of the rope is 0.2kg per meter, the
amount of work done is, (g = 10ms-2)
1) 4000J
2) 4040J
3) 4400J
4) 4200J​

Answer 1

Answer:

Given: Mass of Bucket = 20kg

Linear density of rope = 0.2kg/m

Depth of Well = 20m

Length of Rope Inside the well initially. = 20m

So Inital Mass of Rope = lenght x linear density = 20 x 0.2 = 4kg

Let us take 2 Sytems i.e., bucket and rope separately.

Case i (for Bucket)

Mass of bucket is constant everywhere

Force exerted by bucket = 20 x 10 = 200N

Work Done = F.S = 200 x 20 = 400N

System II : Force Rope

There is a variable mass for rope

Mass of rope at 20 mt depth = 0.2 x 20 = 4 kg

Mass of rope at 19 mt dept = 0.2 x 19 = 3.8 kg

So mass Changes per meter

Let Us Add All the Workdone per meter for 20 mts

W = W1 + W2 + W3..........................W20 (∵Work at 20mt above initial for rope is 0)

W = m1gs + m2gs + m3gs............................m20gs

W = gs(m1 + m2 +m3........................m20)

W = 10(1)(4 + 3.8 + 3.6 + ...................... 0.2 + 0)

W = 10(4 +3.8 +................. 0.2)

We know The Sn = n/2(a + an)

S₂₀ = 20/2(4 + 0.2) ⇒ 42

W= 10(42)

W = 420Nm

By Adding work done of Rope and Bucket We get total Work Done byt the 2 system

i.e W = 4000 + 420 = 4420Nm

∴Total Work Done = 4420Nm