Question

Water is drawn from a well in a 5 kg drum of
capacity 55 L by two ropes connected to the
top of the drum. The linear density of each
rope is 0.5 kgm'. The work done in lifting
water to the ground from the surface of water
in the well 20 m below is (g = 10 ms?)
1)1.4x104J
2)1.5x104J
3) 9.8x6x10 J
4) 18 J​

Answer 1

Answer:

(1) 1.4×10⁴ J

Explanation:

Weight of the empty drum= 5 kg

Capacity of the drum= 55 L

or 55 kg will be the weight of water that can fill the drum

Linear density of two ropes= 0.5 kgm⁻¹

Depth of the well= height to which water and drum are to be lifted= 20 m

Work done in lifting water and drum= W1= mgh=  

    = (mass of empty drum+mass of water)×10×20

    = (5+55)×10×20= 12000 J

Work done in lifting the ropes= W2=?

Mass of the two ropes will be= linear density of ropes×length×2

                                                = 0.5 ×20× 2= 20 kg

As the center of gracity of rope will lift 10m therefore height will be= 10 m

Work done in lifting ropes=W2= mgh= 20×10×10= 2000 J

Total work done in lifting water to ground=

Work done in lifting water and drum + work done in lifting ropes

= W1+W2

= 12000+2000=14000 J = 1.4×10⁴ J

Hope it will be helpful