91影视

The given data can be listed below,

• The mass of a lead sphere is,$m_{Pb}=M$
• The mass of an Aluminium sphere is, $m_{Al}=M$

The density of an object can be used to determine what materials are included within it. The purity of a metal sample can be determined by measuring its density.

The mass of uniform spheres can be given by,

$\begin{array}{l}{m}_{Pb}=V_{Pb}{蚁}_{Pb}\\ m_{Al}=V_{Al}{蚁}_{Al}\end{array}$ 鈥�(颈)

Here, $V_{Pb}$is the volume of lead sphere, $V_{Al}$is the volume of the aluminium sphere, ${蚁}_{Pb}$is the density of lead, and ${蚁}_{Al}$is the density of the Aluminium.

The volume of sphere is given by,

$V=\frac{4\mathrm{蟺}}{3}{r}^3$ 鈥�(颈颈)

Here, r is the radius of sphere.

Substitute the value of volume in equation (i).

$m_{Pb}=\frac{4蟺}{3}{r_{Pb}}^3{蚁}_{Pb}$ 鈥�(颈颈颈)

$m_{Al}=\frac{4\mathrm{蟺}}{3}{r}_{{}_{Al}}^3{蚁}_{Al}$ 鈥�(颈惫)

Equate equation (iii) and (iv), as the mass of both spheres is same.

$\begin{array}{r}\frac{4蟺}{3}{r_{Pb}}^3{蚁}_{Pb}=\frac{4蟺}{3}{r_{AJ}}^3{蚁}_{AI}\\ \frac{r_{AJ}}{r_{Pb}}={\left(\frac{{蚁}_{Pb}}{{蚁}_{AJ}}\right)}^{1/3}\\ ={\left(\frac{11.3}{2.7}\right)}^{1/3}\\ =\frac{1.60}{1}\end{array}$

Thus, the ratio of the radius of aluminium to the radius of lead is 1.60:1