A solid rock, suspended in air by a spring scale, has a measured mass of 8.00 kg. When the rock is submerged in water, the scale reads 3.70 kg. What is the density of the rock? (water density = 1 000 kg/m3)
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Jun 28th, 2015
Volume of water displaced by the rock is equal to the rock’s volume
From Newton’s 2nd law,
the equation for the net forces acting on the rock in air is: 0 = w(air) - mg
Force for the rock in water 0 = B - mg + w(water)
B = mg - w(water)----------------(2)
From 1 & 2 we can write , B = w(air) - w(water) = (8.00) * (9.80) - (3.7 kg)*(9.80) = 42.14 N
Since buoyancy B = ρVg
V = B / ρg = 42.14 / (1000*9.80 ) = 0.0043 m³
Hence volume of the rock = 0.0043 m³ , therefore density of the rock is, ρ = 8 / 0.0043 = 1860.465 kg/m³