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Question
A rubber ball floats in water with 2/7 of its volume above the surface of the water. Calculate the average relative density of the rubber ball.
Solution
Let the volume of rubber ball = V
Volume of rubber ball above the water surface = `2/7`V
Volume of rubber ball below the water surface = `"V" - 2/7`V
`= ("7V" - "2V")/7 = 5/7`V
⇒ Volume of water displayed by the immersed part of the rubber ball = `5/7`V
by the law of floatation:
Volume of rubber ball × density of rubber ball
= Volume of water displayed × density of water
`"V" xx rho = 5/7 "V" xx rho_"w"`
But, `rho_"w" = 1 "g cm"^-3`
`=> "V" xx rho = 5/7 "V" = 1`
`rho = 5/7 = 0.71` g cm-3
Average relative density of rubber ball = `"Density of rubber ball"/"Density of water"`
`= rho/rho_"w" = 0.71/1 = 0.71`
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