Question

On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?

0.40
1.02
1.05
2.51

Answer 1

2.51

Explanation:

Answer 2

Option D. 2.51 is correct.

Explanation:

Magnitude of first earthquake = 8.6

Let intensity of first earthquake be x

`Magnitude = \log((x)/(S)),\text{ where S is seismographic factor}\\\\\implies 8.6=\log((x)/(S)).......(1)`

Magnitude of second earthquake = 8.2

Let intensity of second earthquake be y

`Magnitude = \log((y)/(S)),\text{ where S is seismographic factor}\\\\\implies 8.2=\log((y)/(S)).......(2)`

Now, to find the factor by which intensity of first earthquake is greater than intensity of second : we divide equation (1) by equation (2)

`\implies\log((x)/(y))=8.6 - 8.2\\\\\implies \log((x)/(y))=0.4\\\\\implies(x)/(y)=10^(0.4)\\\\\implies(x)/(y)=2.51`

Hence the required factor is 2.51

Therefore, Option D. 2.51 is correct.