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Two identical spheres S(1) and S(2) out ...

Two identical spheres `S_(1)` and `S_(2)` out of which `S_(1)` is placed on the insulating horizontal surface and `S_(2)` hangs from an insulating string. If both were given same quantity of heat. Then:

A

temperature of `S_(1)` will increase more than `S_(2)`

B

temperature of `S_(2)` will increase more than `S_(1)`

C

Heat given only increases internal energy

D

Heat given not only increases internal energy but goes in other forms also.

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the situation of two identical spheres \( S_1 \) and \( S_2 \) when they are given the same quantity of heat. ### Step-by-Step Solution: 1. **Understanding the Setup**: - Sphere \( S_1 \) is placed on an insulating horizontal surface. - Sphere \( S_2 \) is hanging from an insulating string. - Both spheres are identical and are given the same quantity of heat. **Hint**: Visualize the setup and the forces acting on each sphere. 2. **Effect of Heat on the Spheres**: - When heat is added to a substance, its temperature increases, and it may expand. - The heat added to each sphere will cause them to expand, increasing their radius. **Hint**: Recall the concept of thermal expansion and how heat affects the dimensions of solids. 3. **Change in Potential Energy**: - For \( S_1 \) (on the surface), as it expands, its center of mass remains at the same level (since it is on a horizontal surface), and thus its potential energy does not change significantly. - For \( S_2 \) (hanging), as it expands, its center of mass will move upward, which means its potential energy increases. **Hint**: Consider how the position of the center of mass affects potential energy in both cases. 4. **Heat Distribution**: - The heat given to \( S_1 \) primarily increases its internal energy (temperature) since there is no change in height. - The heat given to \( S_2 \) not only increases its internal energy but also does work against gravity to raise its center of mass, thus increasing its potential energy. **Hint**: Think about how energy conservation applies here and how heat can be converted into different forms of energy. 5. **Conclusion**: - Since \( S_2 \) has to do work to raise its center of mass, the effective increase in internal energy (temperature) will be less than that of \( S_1 \). - Therefore, the temperature of \( S_2 \) will increase less than that of \( S_1 \). **Hint**: Compare the net heat used for internal energy increase in both spheres. ### Final Answer: - The temperature of sphere \( S_2 \) will increase less than that of sphere \( S_1 \) due to the work done against gravity.
To solve the problem, we need to analyze the situation of two identical spheres \( S_1 \) and \( S_2 \) when they are given the same quantity of heat. ### Step-by-Step Solution: 1. **Understanding the Setup**: - Sphere \( S_1 \) is placed on an insulating horizontal surface. - Sphere \( S_2 \) is hanging from an insulating string. - Both spheres are identical and are given the same quantity of heat. ...
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