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The time period of a simple pendulum is given by T=2π(√l/g) The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is:?
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The time period of a simple pendulum is given by T=2π(√l/g) The measur...
Calculation of Percentage Accuracy in Determination of 'g'
- Given values:
- Length of pendulum (l) = 10 cm ± 1 mm = 10 cm ± 0.1 cm
- Time for 200 oscillations (T) = 100 seconds ± 1 second
- Calculating the actual length of the pendulum:
- Actual length = 10 cm ± 0.1 cm = 10 cm
- Converting length to meters: l = 0.1 m
- Calculating the actual time period of one oscillation:
- Time for 1 oscillation = 100 seconds / 200 = 0.5 seconds
- Substituting the values in the formula:
- T = 2π(√l/g)
- 0.5 = 2π(√0.1/g)
- Solving for 'g', we get g = 39.2 m/s²
- Calculating the percentage accuracy in the determination of 'g':
- Percentage error in length = (0.1 / 10) x 100 = 1%
- Percentage error in time = (1 / 100) x 100 = 1%
- Total percentage error:
- Total percentage error = Percentage error in length + Percentage error in time = 1% + 1% = 2%
- Rounding off to the nearest integer:
- The value of 'x' (percentage accuracy) is 2%, rounded to the nearest integer.
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The time period of a simple pendulum is given by T=2π(√l/g) The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is:?
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The time period of a simple pendulum is given by T=2π(√l/g) The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is:? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The time period of a simple pendulum is given by T=2π(√l/g) The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is:? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The time period of a simple pendulum is given by T=2π(√l/g) The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is:?.
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