To find the density of glycerin, we can use the concept of buoyancy. The buoyant force acting on the sphere is equal to the weight of the liquid displaced by the submerged volume of the sphere.
Let the density of the glycerin be ρ kg/m^3, and the volume of the sphere be V m^3. Given that 50% of the sphere is submerged, the volume of the sphere submerged in glycerin is 0.5V.
The buoyant force acting on the sphere is given by:
Buoyant force = Weight of glycerin displaced
ρ*g*0.5V = ρ_glycerin*g*0.5V = ρ_water*g*0.5*V
Since the sphere is in equilibrium, the weight of the sphere is balanced by the buoyant force. The weight of the sphere is given by:
Weight of the sphere = ρ*g*V = ρ*g*V
Setting these two equations equal to each other, we get:
ρ*g*V = ρ_water*g*0.5*V
Solving for the density of glycerin, we get:
ρ = (ρ_water*0.5)
Substitute the given values:
ρ = (1000 kg/m^3 * 0.5)
ρ = 500 kg/m^3
Therefore, the density of glycerin is 500 kg/m^3.
A plastic sphere floats in water with 50 percent of it's volume submerged, find the density of glycerin (Density of water =1000kg/m-3
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