AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper

Consider the small portion of element dx as shown below.

The mass of the element is,
dm‌‌=ρdV
‌‌=ρπr2dx
The potential energy of the mass dm is calculated as,
dU=(dm)gx
dU=gρπr2xdx
Integrate the above equation on both sides.
U=gρπr2‌

20

∫

6

xdx
Substitute the given values in the above equation.
U‌‌=10×103×3.14×(2.5)2[‌

202

2

−‌

62

2

]
‌‌=104×3.14×(2.5)2×182
‌‌=35.71×106J
The time taken by the pump is calculated as,
time‌‌=‌

‌ work done ‌

‌ power ‌

‌‌=‌

35.71×106

10×746×60

‌‌=80min