Question

A uniform copper sphere and a uniform aluminum sphere have the same mass.What is the ratio of the radius of the aluminum sphere to the radius of the zinc sphere? The density of alumnum is 2700 kg/m3 and the density of zinc is 7130 kg/m3 .

Answer 1

Answer:

$\frac{r_{Al}}{r_{Zn} }= 1.625 : 1$

Explanation:

$density = \frac{mass}{volume}$

           ρ =$\frac{m}{v}$

making mass subject of formula we have

  m=ρv

from the question aluminium and zinc have same mass hence we can say;

$m_{Al}=m_{Zn}$

which means;  $ρ_{Al} V_{Al}=ρ_{Zn} V_{Zn}$  

        $\frac{ρ_{Al} }{ρ_{Zn} }= =\frac{V_{Zn} }{V_{Al} }$

  $\frac{ρ_{Al} }{ρ_{Zn} }= =\frac{4\pi r_{Zn} ^{3} }{4\pi r_{Al}^{3} }$

$\frac{ρ_{Al} }{ρ_{Zn} }= =\frac{r_{Zn} ^{3} }{r_{Al}^{3} }$

$\frac{ρ_{Al} }{ρ_{Zn} }= =(\frac{r_{Zn}}{r_{Al} })^{3}$

$\frac{r_{Zn}}{r_{Al} }= \sqrt{\frac{ρ_{Al} }{ρ_{Zn} }}$

${ρ_{Al}= 2700{/tex] [tex]{ρ_{Zn}= 7130{/tex][tex]\frac{r_{Zn}}{r_{Al} }=\sqrt{\frac{2700 }{7130} }}$

$\frac{r_{Zn}}{r_{Al} }= 0.6154$

$\frac{r_{Al}}{r_{Zn} }=\frac{1}{0.6154}$

$\frac{r_{Al}}{r_{Zn} }= 1.625 : 1$