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A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec -
explain why ans 2?
explain why ans 2?
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A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C...
Understanding the Pendulum Clock Mechanism
A pendulum clock operates based on the length of its pendulum, which influences the time it takes to complete one full swing. The length of the pendulum is affected by temperature changes due to thermal expansion.
Effect of Temperature on Pendulum Length
- The coefficient of linear expansion for iron (α) is given as \(10^{-5} / °C\).
- The length of the pendulum, \(L\), increases with temperature according to the formula:
\[
\Delta L = L_0 \cdot \alpha \cdot \Delta T
\]
where:
- \(L_0\) is the original length (1 m),
- \(\Delta T\) is the change in temperature (10°C).
Calculating the Change in Length
- Substituting the values:
\[
\Delta L = 1 \cdot 10^{-5} \cdot 10 = 10^{-4} \, \text{m} = 0.0001 \, \text{m}
\]
- New length \(L = 1 + 0.0001 = 1.0001 \, \text{m}\).
Impact on Time Period
- The time period \(T\) of a pendulum is given by:
\[
T = 2\pi \sqrt{\frac{L}{g}}
\]
- As \(L\) increases, \(T\) will also increase.
Calculating Time Lost
- The increase in time period leads to the clock running slow.
- The approximate change in time (ΔT in seconds per day) can be calculated using the formula:
\[
\Delta T \approx \frac{\Delta L}{L} \cdot (86400 \, \text{seconds}) \quad \text{(for one day)}
\]
- With \(L = 1 \, \text{m}\):
\[
\Delta T \approx \frac{0.0001}{1} \cdot 86400 = 8.64 \, \text{seconds}
\]
Final Conclusion
- The clock will lose approximately 8 seconds per day due to the increase in temperature.
Thus, the correct answer is **A. will lose 8 seconds per day**.
A pendulum clock operates based on the length of its pendulum, which influences the time it takes to complete one full swing. The length of the pendulum is affected by temperature changes due to thermal expansion.
Effect of Temperature on Pendulum Length
- The coefficient of linear expansion for iron (α) is given as \(10^{-5} / °C\).
- The length of the pendulum, \(L\), increases with temperature according to the formula:
\[
\Delta L = L_0 \cdot \alpha \cdot \Delta T
\]
where:
- \(L_0\) is the original length (1 m),
- \(\Delta T\) is the change in temperature (10°C).
Calculating the Change in Length
- Substituting the values:
\[
\Delta L = 1 \cdot 10^{-5} \cdot 10 = 10^{-4} \, \text{m} = 0.0001 \, \text{m}
\]
- New length \(L = 1 + 0.0001 = 1.0001 \, \text{m}\).
Impact on Time Period
- The time period \(T\) of a pendulum is given by:
\[
T = 2\pi \sqrt{\frac{L}{g}}
\]
- As \(L\) increases, \(T\) will also increase.
Calculating Time Lost
- The increase in time period leads to the clock running slow.
- The approximate change in time (ΔT in seconds per day) can be calculated using the formula:
\[
\Delta T \approx \frac{\Delta L}{L} \cdot (86400 \, \text{seconds}) \quad \text{(for one day)}
\]
- With \(L = 1 \, \text{m}\):
\[
\Delta T \approx \frac{0.0001}{1} \cdot 86400 = 8.64 \, \text{seconds}
\]
Final Conclusion
- The clock will lose approximately 8 seconds per day due to the increase in temperature.
Thus, the correct answer is **A. will lose 8 seconds per day**.
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A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec - explain why ans 2?
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A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec - explain why ans 2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec - explain why ans 2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec - explain why ans 2?.
A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec - explain why ans 2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec - explain why ans 2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec - explain why ans 2?.
Solutions for A pendulum clock has an iron pendulum 1 m long ( α iron = 10 − 5 / ∘ C ) ( 𝛼 iron = 10 - 5 / ∘ 𝐶 ) . If the temperature rises by 10 ∘ C 10 ∘ 𝐶 , the clock A. will lose 8 seconds per day B. will lose 4.32 seconds per day C. will gain 8 seconds per day D. will gain 4.32 second per sec - explain why ans 2? in English & in Hindi are available as part of our courses for NEET.
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