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Kinetic energy of a particle depends on the square of speed of the particle . If error in measurement of speed is 40% then error in the measurement of Kinetic energy will be
The answer is 96%?
The answer is 96%?
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Kinetic energy of a particle depends on the square of speed of the par...
Error in Measurement of Kinetic Energy
When measuring the kinetic energy of a particle, it is important to understand how errors in speed affect the overall measurement. Kinetic energy (KE) is given by the formula:
KE = (1/2) mv²
where:
- m = mass of the particle
- v = speed of the particle
Since kinetic energy depends on the square of the speed, any error in speed will have a significant impact on the kinetic energy calculation.
Error in Speed Measurement
If the error in measuring speed (v) is 40%, it means:
- The speed can vary by ±40% of its measured value.
- This results in actual speed values that range from 60% to 140% of the original measurement.
Calculating Error in Kinetic Energy
To find the error in kinetic energy, we can analyze how a percentage change in speed translates to a change in kinetic energy:
- If speed increases by 40%:
- New speed, v' = 1.4v
- KE' = (1/2)m(1.4v)² = (1/2)m(1.96v²) = 1.96 KE
- If speed decreases by 40%:
- New speed, v'' = 0.6v
- KE'' = (1/2)m(0.6v)² = (1/2)m(0.36v²) = 0.36 KE
Conclusion
The errors in kinetic energy can be calculated as follows:
- Maximum increase = 1.96 KE - KE = 0.96 KE (which is 96%)
- Maximum decrease = KE - 0.36 KE = 0.64 KE (which is 64%)
Thus, the overall error in kinetic energy measurement, considering both increases and decreases in speed, can indeed yield an error of up to 96%. This illustrates how sensitive kinetic energy is to changes in speed, particularly with a significant percentage error in measurement.
When measuring the kinetic energy of a particle, it is important to understand how errors in speed affect the overall measurement. Kinetic energy (KE) is given by the formula:
KE = (1/2) mv²
where:
- m = mass of the particle
- v = speed of the particle
Since kinetic energy depends on the square of the speed, any error in speed will have a significant impact on the kinetic energy calculation.
Error in Speed Measurement
If the error in measuring speed (v) is 40%, it means:
- The speed can vary by ±40% of its measured value.
- This results in actual speed values that range from 60% to 140% of the original measurement.
Calculating Error in Kinetic Energy
To find the error in kinetic energy, we can analyze how a percentage change in speed translates to a change in kinetic energy:
- If speed increases by 40%:
- New speed, v' = 1.4v
- KE' = (1/2)m(1.4v)² = (1/2)m(1.96v²) = 1.96 KE
- If speed decreases by 40%:
- New speed, v'' = 0.6v
- KE'' = (1/2)m(0.6v)² = (1/2)m(0.36v²) = 0.36 KE
Conclusion
The errors in kinetic energy can be calculated as follows:
- Maximum increase = 1.96 KE - KE = 0.96 KE (which is 96%)
- Maximum decrease = KE - 0.36 KE = 0.64 KE (which is 64%)
Thus, the overall error in kinetic energy measurement, considering both increases and decreases in speed, can indeed yield an error of up to 96%. This illustrates how sensitive kinetic energy is to changes in speed, particularly with a significant percentage error in measurement.
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Kinetic energy of a particle depends on the square of speed of the particle . If error in measurement of speed is 40% then error in the measurement of Kinetic energy will be The answer is 96%?
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Kinetic energy of a particle depends on the square of speed of the particle . If error in measurement of speed is 40% then error in the measurement of Kinetic energy will be The answer is 96%? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Kinetic energy of a particle depends on the square of speed of the particle . If error in measurement of speed is 40% then error in the measurement of Kinetic energy will be The answer is 96%? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Kinetic energy of a particle depends on the square of speed of the particle . If error in measurement of speed is 40% then error in the measurement of Kinetic energy will be The answer is 96%?.
Kinetic energy of a particle depends on the square of speed of the particle . If error in measurement of speed is 40% then error in the measurement of Kinetic energy will be The answer is 96%? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Kinetic energy of a particle depends on the square of speed of the particle . If error in measurement of speed is 40% then error in the measurement of Kinetic energy will be The answer is 96%? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Kinetic energy of a particle depends on the square of speed of the particle . If error in measurement of speed is 40% then error in the measurement of Kinetic energy will be The answer is 96%?.
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