When the hydrometer of Problem 42 is placed in a liquid whose specific gravity is greater than some minimum value the device floats with part of the glass tube above the liquid level. Consider a hydrometer that has a spherical bulb 2.4 cm in diameter. The glass tube attached to the bulb is 20 cm long and has a diameter of 7.5 mm. The mass of the hydrometer before lead pellets are dropped into the bulb and the tube is sealed is 7.28 g.

(a) What mass of lead should be placed in the bulb so that the hydrometer just floats in a liquid of specific gravity 0.78?

(b) If the hydrometer is now placed in water, what is the length of the tube that shows above the surface of the water?

(c) The hydrometer is placed in a liquid of unknown specific gravity; the length of the tube above the surface of the liquid is 12.2 cm. Determine the specific gravity of the liquid.