The figure shows an iron ball suspended by thread of negligible mass from an upr
ID: 1374137 • Letter: T
Question
The figure shows an iron ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has a height of 5.50 cm, a face area of 12.0 cm2 on the top and bottom, and a density of 0.262 g/cm3, and 1.60 cm of its height is above the water surface. The water has a density of 1000 kg/m3, and the iron has a density of 7900 kg/m3. What is the radius r of the iron ball?
The figure shows an iron ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has a height of 5.50 cm, a face area of 12.0 cm^2 on the top and bottom, and a density of 0.262 g/cm^3, and 1.60 cm of its height is above the water surface. The water has a density of 1000 kg/m^3, and the iron has a density of 7900 kg/m^3. What is the radius r of the iron ball?Explanation / Answer
Let ? be the density of the cylinder (0.262 g/cm3 or 262 kg/m3 ) and ?Fe be the density of the iron (7.9 g/cm3 or 7900 kg/m3 ). The volume of the cylinder is
Vc = 5.5*12 = 66 cm^3 = 66*10^-6 m^3 = 0.000066 m^3
Vs = 3.9*12 = 46.8 cm^3 = 0.0000468 m^3
p*Vc + pFe*Vb = pw*Vs + pw*Vb
262*0.000066 + 7900*Vb = 1000*0.0000468 + 1000*Vb
Vb = 4.276 cm^3
Vb = 4/3 *pi*r^3
r = 0.01006 = 10.07 mm
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