A hollow sphere of radius r is made of metal whose specific gravity is p
Answers
I think you are aaking this, A hollow sphere of radius R is made of metal whose specific gravity is p The sphere will float in water if thickness of wall of the sphere is?
Solution
For the floating of a hollow sphere, the mass of the displaced water has to be larger than that of the actual mass of the hollow sphere.
As we know the density of the material is ρ
.
Area of the hollow sphere can be written as,
A=4πR^2.
where R is the radius of the sphere.
Mass of the hollow sphere can be written as,
ms=A×t×ρ
where t is the thickness of the hollow sphere.
ms=4πR^2×t×ρ
Now we can calculate the volume of the water displaced.
Volume of the water displaced will be equal to the volume of the hollow sphere.
V=4/3πR^3
To find the mass of the water displaced, we can multiply the volume with density of water. As we know the density of water can be written as 1. So, the mass of the water displaced will be equal to,
mw=4/3πR^3
For the floating of hollow sphere, ms ≤ mw
We can assign the values of mass of water displaced and mass of sphere.
⇒4πR^2×t×ρ ≤ 4/3πR^3
Cancel the quantities on both sides.
⇒t×ρ ≤ 1/3R
So, the thickness of the hollow sphere has to be
t ≤ R/3ρ
for the floating purpose.
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