Question

A ball has a diameter of 3.90 cm and average density of 0.0838 g/cm3. What force is required to hold it completely submerged under water? magnitude N direction

Answer 1

Given,

d = 3.9 cm =. r = 1.95 cm ; rho = 0.0838 m/cm^3

volume of the ball = 4/3 pi r^3 = 31.06 cm^3

We know that,

density = mass/volume

mass = density x volume

mass = 0.0838 g/cm^3 x 31.06 = 2.603 g = 2.603 x 10-3 kg

weight of the ball = Wb = 0.026 N

Now the weight of the water displaced would be:

Volume of water displaced would be equal to that of the call so its mass will be:

M(w) = volume x density = 3.1 x 10-5 m^3 x 1000 kg/m^3 = 0.031 kg

Weight of water = Ww= 0.031 x 9.8 = 0.304 N

Net force on the ball would be:

Fnet = Ww - Wb = 0.304 - 0.026 = 0.278 N

Hence, the force required to hold = Fnet = 0.278 N.