Question

A ball has a diameter of 3.77 cm and average density of 0.0839 g/cm3. What force is required to hold it completely submerged under water?
magnitude _________ N

Answer 1

Answer:

0.25 N

Explanation:

The density of the ball ($\rho_b$) = 0.0839 g/cm³ = 83.9 kg/m³

The density of water ($\rho_w$) = 1000 kg/m³

diameter = 3.77 cm = 0.0377 m

radius of ball = 0.0377/2 = 0.01885 m

The volume (V) = $\frac{4}{3} \pi r^3=\frac{4}{3}*\pi*0.01885^3=2.8*10^{-5}\ m^3$

Let us assume the acceleration due to gravity (g) = 9.8 m/s²

Hence:

The force is required to hold it completely submerged under water (F) is:

$F=\rho_w Vg-\rho_b Vg=1000*(2.8*10^{-5})*9.81-83.9*(2.8*10^{-5})*9.81$

F = 0.25 N