Question

Let ρAl represent the density of aluminum and ρFe that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius rFe on an equal-arm balance. (Use any variable or symbol stated above as necessary.)

Answer 1

ρAl ρFe
let the radius of aluminimu= rAl
radius of iron = rFe
Volume of iron sphere
\[ Viron= 4/3 {\pi} {rFe}^3\]
\[ Valu= 4/3 \pi {rAl}^3\]
we now mass is geiven as= density * volume
Miron= Malum
so
\[ ρFe * 4/3 \pi {rfe}^3= ρAl * 4/3 \pi {rAl}^3\]
or
\[ rAl = rfe \sqrt[3] { ρFe/ρAl }\]