In sport meet the timing of a 200 m straight dash is recorded at the finish point by starting an accurate stop watch on hearing the sound of starting gun firen at the starting poing. The time recorded will be more accurate

Options

A. (a)In winter
B. (b)in summer
C. (c)in all seasons
D. (d)none of these

Explanation

**Step-by-Step Solution:**

1. **Understanding the Problem:**
The problem states that during a 200 m dash, the timing is recorded when the sound of the starting gun reaches the finish line. We need to determine in which season (winter, summer, or all seasons) the timing will be more accurate.

2. **Concept of Sound Velocity:**
The speed of sound in air is influenced by temperature. The velocity of sound (v) in a gas can be expressed as:
\[ v = \sqrt{\frac{\gamma \cdot R \cdot T}{M}} \]
where:
- \( \gamma \) = adiabatic index (ratio of specific heats)
- \( R \) = universal gas constant
- \( T \) = absolute temperature in Kelvin
- \( M \) = molecular mass of the gas

3. **Effect of Temperature on Sound Speed:**
From the equation, we can see that the speed of sound is directly proportional to the square root of the absolute temperature (T). This means that as the temperature increases, the speed of sound also increases.

4. **Comparing Seasons:**
- In summer, the temperature is higher, which means the speed of sound will be greater.
- In winter, the temperature is lower, resulting in a lower speed of sound.

5. **Time Calculation:**
The time taken for the sound to travel from the starting point to the finish line can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed of Sound}} \]
Since the distance is constant (200 m), a higher speed of sound in summer will result in a shorter time for the sound to reach the finish line compared to winter.

6. **Conclusion:**
Therefore, the time recorded at the finish point will be more accurate in summer because the sound will reach the finish line more quickly due to the higher speed of sound in warmer temperatures.

7. **Final Answer:**
The time recorded will be more accurate in **summer**.

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