Four bodies of specific heats `s_1,s_2,s_3 and s_4` are cooled in the same surroundings. If `s_2 gt s_2 gt s_3 gt s_4`, and temperature of all the four bodies is the same, then the specific heat of body which cools fastest, will be –

Options

A. `s_1`
B. `s_2`
C. `s_3`
D. `s_4`

Answer

To solve the problem, we need to analyze the relationship between specific heat and the rate of cooling of the bodies.

### Step-by-Step Solution:

1. **Understand the Problem**: We have four bodies with specific heats \( s_1, s_2, s_3, \) and \( s_4 \) such that \( s_1 > s_2 > s_3 > s_4 \). All bodies are at the same initial temperature and are cooled in the same surroundings.

2. **Apply Newton's Law of Cooling**: According to Newton's Law of Cooling, the rate of change of temperature of an object is proportional to the difference in temperature between the object and its surroundings. However, in this case, we will relate it to the specific heat of the bodies.

3. **Relate Specific Heat to Cooling Rate**: The specific heat \( s \) of a body is defined as the amount of heat required to change the temperature of the body by one degree. The higher the specific heat, the more heat is required to change the temperature, which means the body will cool down more slowly.

4. **Identify the Relationship**: Since the specific heats are given in descending order \( s_1 > s_2 > s_3 > s_4 \), it implies that:
- Body with specific heat \( s_1 \) will cool the slowest.
- Body with specific heat \( s_4 \) will cool the fastest.

5. **Conclusion**: Therefore, the body that cools the fastest is the one with the lowest specific heat, which is \( s_4 \).

### Final Answer:
The specific heat of the body which cools fastest will be \( s_4 \).

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