To solve this problem, it is necessary to apply the concepts related to Newton's second Law as well as to the expression of mass as a function of Volume and Density.
From Newton's second law we know that
F= ma
Where,
m = mass
a = acceleration
At the same time we know that the density is given by,
[tex]\rho = \frac{m}{V} \rightarrow m = \rho V[/tex]
Our values are given as,
[tex]g = 9.8m/s^2[/tex]
[tex]m =0.459 kg[/tex]
D=0.242 m
Therefore the Force by Weight is
[tex]F_w = mg[/tex]
[tex]F_w = 0.459kg * 9.8m/s^2 = 4.498N[/tex]
Now the buoyant force acting on the ball is
[tex]F_B=\rho V g[/tex]
The value of the Volume of a Sphere can be calculated as,
[tex]V = \frac{4}{3} \pi r^3[/tex]
[tex]V = \frac{4}{3} \pi (0.242/2)^3[/tex]
[tex]V = 0.007420m^3[/tex]
[tex]\rho_w = 1000kg/m^3 \rightarrow[/tex] Normal conditions
Then,
[tex]F_B=0.007420*(1000)*(9.8) = 72.716 N[/tex]
Therefore the Force net is,
[tex]F_{net} = F_B -F_w[/tex]
[tex]F_{net} = 72.716N - 4.498N =68.218 N[/tex]
Therefore the required Force is 68.218N
