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A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is δT = 0.01 second and he measures the depth of the well to be L = 20 meters. Take the acceleration due to gravity g = 10 ms–2and the velocity of sound is 300 ms–1. Then the fractional error in the measurement, δL/L, is closest to
  • a)
    0.2 %
  • b)
    5 %
  • c)
    3 %
  • d)
    1 %
Correct answer is option 'D'. Can you explain this answer?
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A person measures the depth of a well by measuring the time interval b...
Total time taken
is also small, so taking binomial approximation
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A person measures the depth of a well by measuring the time interval b...
Dependent on various factors such as the accuracy of his timing device, his reaction time, and the speed of sound in the well.

If the person is using a precise timing device, the error in his measurement of time may be minimal. However, if he is using a less accurate device or relying on his own reaction time, the error could be larger.

Additionally, the speed of sound in the well may not be constant and could vary depending on the temperature, humidity, and other factors. This variability could introduce further error into the measurement.

Overall, the error in the person's measurement of time could range from negligible to significant, depending on the specific circumstances and variables involved.
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A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is δT = 0.01 second and he measures the depth of the well to be L = 20 meters. Take the acceleration duetogravity g = 10 ms–2and the velocity of sound is 300 ms–1. Then the fractional error in the measurement, δL/L, is closest toa)0.2 %b)5 %c)3 %d)1 %Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is δT = 0.01 second and he measures the depth of the well to be L = 20 meters. Take the acceleration duetogravity g = 10 ms–2and the velocity of sound is 300 ms–1. Then the fractional error in the measurement, δL/L, is closest toa)0.2 %b)5 %c)3 %d)1 %Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is δT = 0.01 second and he measures the depth of the well to be L = 20 meters. Take the acceleration duetogravity g = 10 ms–2and the velocity of sound is 300 ms–1. Then the fractional error in the measurement, δL/L, is closest toa)0.2 %b)5 %c)3 %d)1 %Correct answer is option 'D'. Can you explain this answer?.
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