Donald Duck and his nephews manage to sink Uncle Scrooge's yacht (m = 4843 kg), which is made of steel (ρ = 7850 kg/m3). In typical comic-book fashion, they decide to raise the yacht (which is now on the bottom of a lake) by filling it with ping-pong balls. A ping-pong ball has a mass of 2.70 g and a volume of 3.35·10-5 m3.

Question

Donald Duck and his nephews manage to sink Uncle Scrooge's yacht (m = 4843 kg), which is made of steel (ρ = 7850 kg/m3). In typical comic-book fashion, they decide to raise the yacht (which is now on the bottom of a lake) by filling it with ping-pong balls. A ping-pong ball has a mass of 2.70 g and a volume of 3.35·10-5 m3. 
 
How many balls are required to float the ship?

drwls · Answer

The amount of mass that each ball will lift is (in grams)
Pwater*V - Mball
= 1.00 g/cm^3)*3.35*10^1 cm^3 - 2.70
= 30.8 g

The number of pingpong balls needed is 4843*10^3g/30.8 = 157,200

The density of steel does not matter. The answer depends upon the total mass that must be lifted.