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Question: A metallic sphere of mass \(0.2kg\) and volume \(2.5 \times {10^{ - 4}}{m^3}\)is completely immers...

A metallic sphere of mass 0.2kg0.2kg and volume 2.5×10−4m32.5 \times {10^{ - 4}}{m^3}is
completely immersed in the water. Find the buoyant force exerted by water on the sphere.
Density of water = 1000kg/m31000kg/{m^3}

Explanation

Solution

When any object is kept in water some factors like density and other factors like buoyant force cause objects to float on the surface of water. Buoyant force is a force that makes any object float on a water surface .This buoyant force generally equals the weight of displaced water.

Step by step answer: Given: volume of completely immersed sphere = v=2.5×10−4m3v = 2.5 \times {10^{ - 4}}{m^3}
Mass of the metallic sphere = ms=0.2kg{m_s} = 0.2kg
Density of water = d=1000kg/m3d = 1000kg/{m^3}
When any object is kept in water some factors like density and other factors like buoyant force cause objects to float on the surface of water.
Here,
Volume of the water displacement = volume of completely immersed sphere
Volume of the water displacement = v=2.5×10−4m3v = 2.5 \times {10^{ - 4}}{m^3}
Mass of the displaced water = volume  of  completely  immersed  sphere×Density  of  watervolume{\rm{ }}\;of{\rm{ }}\;completely{\rm{ }}\;immersed{\rm{ }}\;sphere \times Density{\rm{ }}\;of{\rm{ }}\;water
Mass of the displaced water = 2.5×10−42.5 \times {10^{ - 4}} ×1000 \times 1000
Mass of the displaced water = 0.25kg0.25kg
Weight of the displaced water is given by-
Mass  of  the  displaced  water×The  acceleration  due  to  gravity  for  earths  surfaceMass{\rm{ }}\;of{\rm{ }}\;the{\rm{ }}\;displaced{\rm{ }}\;water \times The{\rm{ }}\;acceleration{\rm{ }}\;due{\rm{ }}\;to{\rm{ }}\;gravity{\rm{ }}\;for{\rm{ }}\;earths{\rm{ }}\;surface
The acceleration due to gravity for earth’s surface is 9.8m/s29.8m/{s^2}
Weight of the displaced water = 0.25×9.80.25 \times 9.8
Weight of the displaced water = 2.45N2.45N
Since we know buoyant force equals to the weight of displaced water,
Buoyantforce=Weight  of  the  displaced  water=2.45NBuoyant{\rm{ }}force{\rm{ }} = {\rm{ }}Weight{\rm{ }}\;of{\rm{ }}\;the{\rm{ }}\;displaced{\rm{ }}\;water{\rm{ }} = 2.45N

Note: There are three types of buoyant forces:
-Positive buoyancy: Positive buoyancy is when the immersed object is lighter than the fluid displaced and this is often the rationale why the thing floats.
-Negative buoyancy: Negative buoyancy is when the immersed object is denser than the fluid displaced which ends up within the sinking of the thing
-Neutral buoyancy: Neutral buoyancy takes place when the load of an immersed object is adequate to the fluid displaced. Dive taken by the diver is a perfect example for neutral buoyancy.