Answer:
Radius of aluminium sphere which has same mass as of sphere of iron with radius 14 m is 40.745 meters.
Explanation:
Let the radius of aluminium sphere be [tex]r_{a}[/tex]
From the relation between density, mass and volume we know that
[tex]Mass=Density\times volume...............(i)[/tex]
Applying equation 'i' separately to iron and aluminium sphere we get
[tex]M_{a}=\rho _{a}\times V_{a}[/tex]
[tex]M_{ir}=\rho _{ir}\times V_{ir}[/tex]
Equating the masses of iron and aluminium spheres we get
[tex]M_{a}=M_{ir}[/tex]
[tex]\rho _{a}\times \frac{4\pi r_a^3}{3}=\rho _{ir}\times \frac{4\pi r_{ir}^3}{3}[/tex]
[tex]\rho _{a}\times r_{a}^3=\rho _{ir}\times r_{ir}^{3}\\\\\therefore r_{a}=(\frac{\rho _{ir}}{\rho _{a}})^{1/3}\cdot r_{ir}\\\\r_{a}=\frac{7.8610}{2.701}\times 14\\\\\therefore r_a=40.745m[/tex]
