Answer:
32I
Explanation:
Data provided in the question:
Rotational inertia of a sphere about an axis through the center = I
Now,
Let the radius of the sphere be 'R'
also,
Rotational inertia = MR²
Here,
M is the mass
Mass = Density ÷ Volume
Volume of sphere = [tex]\frac{4}{3}\pi R^3[/tex]
Therefore,
M = Density × [tex]\frac{4}{3}\pi R^3[/tex]
Thus,
I = [tex]\text{Density}\times{\frac{4}{3}\pi R^3}\times R^2[/tex]
Now for the sphere of radius twice the radius i.e 2R
Volume = [tex]\frac{4}{3}\pi (2R^3)=\frac{4}{3}\pi\times8R^3[/tex]
Since the density is same
Mass = [tex]\text{Density}\times\frac{4}{3}\pi8R^3[/tex]
Thus,
I' = [tex]\text{Density}\times{\frac{4}{3}\pi 8R^3}\times (2R)^2[/tex]
or
I' = 8 × 4 × [tex]\text{Density}\times{\frac{4}{3}\pi R^3}\times R^2[/tex]
or
I' = 32I
