Question

An open cylindrical tank 2m in diameter and 2m high contains water upto 1.5 m depth. Then the maximum angular speed at which it can be rotated about its vertical axis without any spill of water

Answer 1

Answer:

Cos⁻¹(1/4) or 75.5°

Explanation:

An open cylindrical tank 2m in diameter and 2m high contains water upto 1.5 m depth. Then the maximum angular speed at which it can be rotated about its vertical axis without any spill of water

Volume of Tank = πR²h

R = Diameter /2 = 2/2 = 1 m

h = 2 m

=  πR²h

=  π*1²*2

= 2π m³

contains water upto 1.5 m depth => 2 - 1.5 = 0.5 m height

Volume of Water = 0.5 π m³   as h = 0.5 m

Let say  it can be rotated about its vertical axis at an angle α

Then Volume of water which will not spill = πR²hCosα

= 2πCosα

2πCosα = 0.5 π

=> Cosα = 1/4

=> α = Cos⁻¹(1/4)

=> α = 75.5°