A device to measure the density of a liquid is made of solid plastic with uniform density and has the shape of a sphere with an attached cylinder. The mass of the device is M = 27 g, the volume of the sphere is Vs = 25 cm3, the length of the cylinder is L = 6 cm, and the cross sectional area of the cylinder is A = 0.5 cm2.
The device floats in water (density 1.0 g/cm3) and we are interested in the height h of the cylinder above the water surface.
a) What do you know about the magnitude of the buoyant force FB and the force of gravity Fg ?
[1] FB > Fg [2] FB = Fg [3] FB < Fg [4] need more information to decide
(b) What is the volume of the liquid displaced by the device?
[1] Vdisp = 13.5 cm3 [2] Vdisp = 25 cm3 [3] Vdisp = 27 cm3
[4] Vdisp = 33 cm3 [5] none of these
(c) What is the height of the cylinder above water?
[1] h = 0.5 cm [2] h = 2.0 cm [3] h = 4.0 cm [4] h = 6.0 cm [5] none of these
(d) If the device is put in a liquid with a density larger than the density of water, the height above the liquid surface
[1] increases [2] stays the same [3] decreases [4] need more information to decide