Respuesta :
Answer:[tex]\eta =325.73\times 10^{-3}=0.325 kg/m-s[/tex]
Explanation:
Given
density[tex](\rho )=7.8\times 10^3 kg/m^3[/tex]
Diameter(d)=2.4 mm
time taken=10 s
Distance moved(h)=0.75 m
At terminal velocity Drag force is equal to Weight
[tex]F_D=mg[/tex]
Volume of ball[tex]=\frac{4\pi r^3}{3}=7.23 mm^3[/tex]
Mass of ball[tex]=\rho v=7.23\times 7.8\times 10^3\times 10^{-9}=56.39\times 10^{-6} kg[/tex]
[tex]F_D=56.39\times 10^{-6}\times 9.8=552.66\times 10^{-6} N[/tex]
Also for spherical bodies drag force is equal to Stock Force
[tex]F_s=6\times \pi \times \eta \times r\times v_r[/tex]
Where [tex]v_r[/tex]= Terminal velocity
[tex]v=\frac{h}{t}=\frac{0.75}{10}=0.075 m/s[/tex]
[tex]552.66\times 10^{-6}=6\times pi\times \eta \times \1.2\times 10^{-3}\times 0.075[/tex]
[tex]\eta =325.73\times 10^{-3}=0.325 kg/m-s[/tex]
