Questions and Answers
What is the rate of decay when the number of active nuclei is No/2?
What is the relationship between the sag in the wire and the tension due to its weight?
How is the speed of the transverse wave on the wire related to parameters L, d, and g?
What expression best represents the total mechanical energy of the vibrating string when plucked?
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At what condition does the sag in the wire minimize relative to its length L?
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Study Notes
Radioactive Decay
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Radioactive decay follows the equation N = Nokt², where:
- N = instantaneous number of active nuclei
- No = initial number of active nuclei
- k = positive constant
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Given the condition t ≤ √(No/2), determine the correct rates of decay as the number of active nuclei decreases to No/2.
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Rate of decay options at N = No/2:
- Option (A): Rate is √kNo
- Option (B): Rate is 2√kNo
- Option (C): Rate is √(kNo/2)
- Option (D): Rate is √3kNo
Wire Sagging
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A wire with mass per unit length µ and fixed length L is tethered between two vertical walls separated by L.
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The wire's own weight causes a sag in its midpoint, designated as d.
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Understanding the sag is essential for analyzing forces and tensions acting on the wire.
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Description
Test your understanding of radioactive decay with this quiz focusing on mathematical problems related to hypothetical radioactive substances. Evaluate the rate of decay based on given conditions and choose the correct options provided. Perfect for physics students looking to solidify their grasp of decay concepts and equations.
