Question

The radius of a well is 7m.water in it is at a depth of 20m and depth of water column is 10m.work done in pumping out water completely from the well is,(g = 10m/s2)
1)38.5MJ 2)38KJ 3)46.2MJ 4)385MJ

Answer 1

$\huge\underline\blue{\rm Answer}$

$\large\red{\boxed{\sf Work\:Done=38.5MkJ}}$

$\huge\underline\blue{\rm Solution:}$

$\large\underline\pink{\sf Given: }$

• Radius (r) = 7m

• Depth = 20m

• Depth of water column (h) = 10m

• g = $\sf{10m/s^2}$

$\large\underline\pink{\sf To\:Find: }$

• Work done in pumping out water completely from the well = ?

━━━━━━━━━━━━━━━━━━━━━━━━

Total mass of water = m

m = density × Volume

$\large\implies{\sf 1000×πr^2h }$

$\large\implies{\sf 1000×\frac{22}{7}×7^2×10}$

$\large\implies{\sf 1540000kg}$

By using centre of mass , centre of mass of water is at depth of (20+5)h from the top

Hence ,

Work done (WD)= mg(20+5)

$\large\implies{\sf 150000×(20+5)}$

$\large\implies{\sf 38500000J}$

$\huge\red{♡}$$\large\red{\boxed{\sf Work\:Done=38.5MkJ}}$