Chapter 12.8, Problem 2ST

To determine

To calculate: The mass of a silver coin $4$ cm in the radius and $0.3$ cm thick. And a silver coin $2$ cm in radius and thick has a mass of $26.4$ g.

Answer to Problem 2ST

The mass of the circular motion is: $158.4\text{g}$ .

Explanation of Solution

Given information:

The mass of a circular coin varies jointly as the thickness and the square of the radius of the coin.

The mass of a silver coin $4$ cm in the radius and $0.3$ cm thick. And a silver coin $2$ cm in radius and thick has a mass of $26.4$ g.

Formula used:

For varies jointly:

  $M=Kt{r}^2$

Calculation:

Consider that, The mass of a silver coin $4$ cm in the radius and $0.3$ cm thick. And a silver coin $2$ cm in radius and thick has a mass of $26.4$ g.

Recall that for varies jointly:

  $M=Kt{r}^2$

The values are:

  $M=26.4,t=0.2,r=2$

Here $M$ is a mass of circular motion and $t,r$ are the thickness and the radius of the coin.

Therefore, the value of $k$ is,

  $\begin{array}{c}M=Kt{r}^2\\ 26.4=K\times 0.2\times 2^2\\ K=\frac{26.4}{0.2\times 4}\\ K=3.3\end{array}$

Now to find the value of $r$ ,

  $M_2=K{t}_2{r}_2{}^2$

The values are:

  $K=3.3,t_2=0.3,r_2=4$

Hence, when:

  $\begin{array}{c}{M}_2=K{t}_2{r}_2{}^2\\ M_2=3.3\times 0.2\times 4^2\\ M_2=3.3\times 0.2\times 16\\ M_2=15.84\text{cm}\end{array}$

Covert centimeter into germs then:

  $\begin{array}{l}{M}_2=15.84\text{cm}\\ {\text{M}}_2=158.4\text{g}\end{array}$

Thus, the mass of the circular motion is: $158.4\text{g}$ .