Answer:
The force needed to hold the ball completely submerged is 0.323N
Explanation:
In this question we have given,
diameter of ball= 4.1 cm
Therefore, radius of ball, [tex]r=\frac{4.1}{2} cm[/tex]
[tex]r=\frac{4.1}{2\times 100} m[/tex]
[tex]r=.0205 m[/tex]
density of ball, [tex]\rho_{b}=0.0841 gcm^{-3}[/tex]
[tex]\rho_{b}=84.1 kgm^{-3}[/tex]
density of water,[tex]\rho_{w}=1000kgm^{-3}[/tex]
we know that, volume of sphere is given by following formula,
[tex]V=\frac{4\pi\times r^3}{3}[/tex]
we know that,
[tex]density=\frac{mass}{volume}\\ mass=density \times volume[/tex]
Therefore,
[tex]mass\times gravity =density \times volume \times gravity[/tex]
or
[tex]Force =density \times volume \times gravity[/tex]..............(1)
Here,
[tex]density= \rho_{w}-\rho_{b}[/tex]
Put values of density, volume and gravity in equation (1)
[tex]Force =(\rho_{w}-\rho_{b}) \times \frac{4\pi\times \frac{4.1}{2}}{3}\times 9.8[/tex].
[tex]Force =(1000-84.1}) \times\frac{4 \pi \times (.0205)^3 \times 9.8}{3}[/tex]
Force=0.323N
the force needed to hold the ball completely submerged is 0.323N
