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

Answer:

Option D. 2.51 is correct.

Step-by-step explanation:

Magnitude of first earthquake = 8.6

Let intensity of first earthquake be x

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

Magnitude of second earthquake = 8.2

Let intensity of second earthquake be y

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

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

$\implies\log(\frac{x}{y})=8.6 - 8.2\\\\\implies \log(\frac{x}{y})=0.4\\\\\implies\frac{x}{y}=10^{0.4}\\\\\implies\frac{x}{y}=2.51$

Hence the required factor is 2.51

Therefore, Option D. 2.51 is correct.