Earthquakes at two places P and Q were measured by a seismograph which recorded the magnitude as 2 and 6. The magnitude of tremors at P and Q can be compared as

Options

A. Tremors at Q are three times those at place P
B. Tremors at Q are six times those at place P
C. Tremors at Q are 1000 times those at place P
D. Tremors at Q are 10000 times those at place P

Explanation

To compare the magnitudes of tremors at places P and Q, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Magnitude Scale**:
The magnitude of an earthquake is measured on a logarithmic scale. This means that each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release.

2. **Identify the Magnitudes**:
- Magnitude at P (M_P) = 2
- Magnitude at Q (M_Q) = 6

3. **Calculate the Difference in Magnitude**:
The difference in magnitude between Q and P is:
\[ M_Q - M_P = 6 - 2 = 4 \]

4. **Calculate the Ratio of Tremors**:
Since the scale is logarithmic, the ratio of the tremors can be calculated using the formula:
\[ \text{Tremor at Q} = 10^{(M_Q - M_P)} \times \text{Tremor at P} \]
Substituting the values:
\[ \text{Tremor at Q} = 10^{(6 - 2)} \times \text{Tremor at P} = 10^4 \times \text{Tremor at P} \]

5. **Conclusion**:
This means that the tremor at Q is 10,000 times stronger than the tremor at P. Therefore, we can conclude that:
\[ \text{Tremor at Q} = 10^4 \times \text{Tremor at P} \]

### Final Answer:
The tremor at Q is 10,000 times greater than the tremor at P.

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