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Question: A fire wood board floats in fresh water with 60% of its volume under water. The density of wood in \...

A fire wood board floats in fresh water with 60% of its volume under water. The density of wood in g/cm3g/c{m^3} is:
A) 0.4
B) 0.5
C) 0.6
D) <0.4

Explanation

Solution

In this question we are going to use the concept of buoyant force because buoyant force is the one that causes an object to float. Buoyant force on an object is given by following formula,
Buoyant force = density of substance×total volume×g{\text{Buoyant force = density of substance}} \times {\text{total volume}} \times g

Schematic diagram of wood board immersed in water

Complete step by step solution:
Let the density of substance is ρ\rho and density of water is ρ′{\rho '} a total volume of substance is V and volume under water is V′{{\text{V}}'}
By the definition of buoyant force we know that
Buoyant force= mass of water displaced
density of substance×total volume×g=volume under water×density of water×g{\text{density of substance}} \times {\text{total volume}} \times g = {\text{volume under water}} \times {\text{density of water}} \times {\text{g}}
⇒ρ×V×g=V′×ρ′×g\Rightarrow \rho \times {\text{V}} \times g = {{\text{V}}'} \times {\rho '} \times {\text{g}}……. (1)
As we know that the density of water is 1g/cm31g/c{m^3}
From equation (1),
⇒ρ=V′×ρ′V\Rightarrow \rho = \dfrac{V' \times \rho '}{V}
As it is given in the question that 60% volume of substance is under water so V′=0.6V{V'} = 0.6V
Putting the values of V′,ρ′and V{{\text{V}}'},{\rho '}{\text{and }}V
⇒ρ=0.6V×1V\Rightarrow \rho = \dfrac{{0.6V \times 1}}{{\text{V}}}
⇒ρ=0.6g/cm3\Rightarrow \rho = 0.6g/c{m^3}

The density of wood is ρ=0.6g/cm3\rho = 0.6g/c{m^3}.

Note: In this question we have used the concept buoyant force. This is a force which helps a matter to float in the water. This force exerts on a body when it is partially or wholly immersed in water. Buoyant force acts on the body due to the difference in pressure on opposite sides of a body. Buoyant force is also known as upthrust because it acts in upward direction. The point where buoyant force acts is called the centre of buoyancy. Buoyant force is the reason that an object floats or sinks in water. Buoyant force depends on the volume of the body immersed and density of fluid. It is due to buoyant force that humans can swim, fish, icebergs, ships etc. can float in water.