Chapter MPS, Problem 8.5MPS

(a)

To determine

To Find: The movement of ground in an earthquake.

Answer to Problem 8.5MPS

  $100000$

Explanation of Solution

Given:

Movement $=M$

Richter Scale $=R$

  $R={\log }_{10}M$

  $R=5$

Formula Used:

  $R={\log }_{10}M$

  $\begin{array}{l}\\ a={10}^b\\ \text{On applying log both side}\\ {\log }_{10}a=b\end{array}$

Calculation:

  $\begin{array}{l}R={\log }_{10}M\\ R=5\\ \Rightarrow {10}^R=M\\ \Rightarrow M={10}^5\\ \Rightarrow M=100000\end{array}$

Conclusion:

Thus the movement to an earthquake is $100000$ .

(b)

To determine

To Find: The change in movement of earth if there is change Richter scale.

Answer to Problem 8.5MPS

  $100$

Explanation of Solution

Given:

Movement $=M$

Richter Scale $=R$

  $R={\log }_{10}M$

  $R=5$

  $R=3$

Formula Used:

  $R={\log }_{10}M$

  $\begin{array}{l}\\ a={10}^b\\ \text{On applying log both side}\\ {\log }_{10}a=b\end{array}$

Calculation:

  $\begin{array}{l}R={\log }_{10}M\\ R=5\\ \Rightarrow {10}^R=M\\ \Rightarrow M={10}^5\\ \Rightarrow M=100000\\ R=3\\ \Rightarrow M={10}^3\\ \Rightarrow M=1000\\ \frac{R=5}{R=3}=\frac{100000}{1000}=100\\ \Rightarrow \left(R=5\right)=\left(R=3\right)\times 100\end{array}$

Conclusion:

Thus, the change is 100 times.