volume of ball?

Question

A 10 kg ball weighs 98 N in air and weighs 65 N when submerged in water. The volume of the ball is??

please help, thanks

Answer 1

Since the density of air is so low, it is a very good estimate to say that the difference in the weight of the ball in air and in water is the weight of the water which is displaced by the ball when it is submerged. Technically, there is a very slight buoyant force acting on the ball even when it is in the air, but this is totally negligible compared to the buoyant force acting on the ball in the water.

The difference in the apparent weight of the ball is 98 Newtons – 65 Newtons = 33 Newtons.
So the ball displaces 33 Newtons worth of water when submerged…that is the weight of the water it displaced. To find the mass of the water which is displaced, divide by 9.8 m/s^2 to get 3.37 kg of water.

Water has a density of 1 kg per Liter.
So 3.37 kg of water would have a volume of 3.37 Liters.

Thus the ball has a volume of 3.37 Liters (or .00337 cubic meters).


If you want to get technical,
the volume of the ball will be:
V = W_diff / (g * (ρ_water – ρ_air))
Where W_diff is the difference in the apearant weight of the ball, g is the gravitational acceleration experience by the ball, and ρ_water and ρ_air are the densities of water and air respectively.

W_diff = 33 Newtons
g = 9.81 m/s^2
ρ_water = 1 kg / Liter
ρ_air = .0012 kg / Liter

But since the density of air is so low compared to water, we still get the same answer as we do assuming that the ball weighs 98 Newtons in a vacuum.

Answer 2

Reduction in weight is due to buoyancy, which is 33 N. Volume of the ball is equal to the volume of the water displaced and that is equal to the mass of the water which is

33/9.8 = 3.367 kg and so the volume is 3.367 litres

Answer 3

Depends on how brave you are.