Answer:
26 cm
Explanation:
V = Volume
R = Outer radius = 58.7 cm
r = Inner radius
g = Acceleration due to gravity = 9.81 m/s²
[tex]\rho[/tex] = Density
Force on shell
[tex]F=v\rho g\\\Rightarrow F=\frac{4}{3}\pi R^3\times 1000g[/tex]
Weight of the shell
[tex]W=\frac{4}{3}\pi (R^3-r^3)\times 7870g[/tex]
Equating the two equations as the forces are conserved
[tex]\frac{4}{3}\pi R^3\times 1000g=\frac{4}{3}\pi (R^3-r^3)\times 7870g\\\Rightarrow R^3\times 1000=(R^3-r^3)\times 7870\\\Rightarrow R^3=(R^3-r^3)\frac{7870}{1000}\\\Rightarrow R^3=(R^3-r^3)7.87\\\Rightarrow 6.87R^3=r^37.87\\\Rightarrow r=\left(\frac{6.87}{7.87}\times0.587^3\right )^{\frac{1}{3}}\\\Rightarrow r=0.561\ m[/tex]
Inner radius is 0.561 m
The thickness of the wall is 0.587-0.561 = 0.026 m = 26 cm
