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The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g?
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The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measur...
Calculation of g
The formula for the period of oscillation of a simple pendulum is T=2πL/g−−−−√, where L is the length of the pendulum and g is the acceleration due to gravity. Rearranging the formula, we get g=4π^2L/T^2.
Accuracy in L
The measured value of L is 20.0cm known to 1mm accuracy. This means that the actual length of the pendulum could be anywhere between 19.9cm and 20.1cm. We can take the average of these values as the true value of L, which is 20.0cm.
Accuracy in T
The time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch of 1 s resolution. This means that the actual time taken for 100 oscillations could be anywhere between 89.5 s and 90.5 s. We can take the average of these values as the true value of T, which is 90 s.
Accuracy in g
Using the formula g=4π^2L/T^2, and substituting the values of L and T, we get g=9.86 m/s^2. To find the accuracy in the determination of g, we need to find the maximum and minimum possible values of g based on the uncertainties in L and T.
The maximum possible value of g can be found by using the minimum value of L (19.9cm) and the maximum value of T (90.5 s), which gives g=9.69 m/s^2. The minimum possible value of g can be found by using the maximum value of L (20.1cm) and the minimum value of T (89.5 s), which gives g=10.03 m/s^2.
Therefore, the accuracy in the determination of g is ±0.17 m/s^2, which is the difference between the maximum and minimum possible values of g.
The formula for the period of oscillation of a simple pendulum is T=2πL/g−−−−√, where L is the length of the pendulum and g is the acceleration due to gravity. Rearranging the formula, we get g=4π^2L/T^2.
Accuracy in L
The measured value of L is 20.0cm known to 1mm accuracy. This means that the actual length of the pendulum could be anywhere between 19.9cm and 20.1cm. We can take the average of these values as the true value of L, which is 20.0cm.
Accuracy in T
The time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch of 1 s resolution. This means that the actual time taken for 100 oscillations could be anywhere between 89.5 s and 90.5 s. We can take the average of these values as the true value of T, which is 90 s.
Accuracy in g
Using the formula g=4π^2L/T^2, and substituting the values of L and T, we get g=9.86 m/s^2. To find the accuracy in the determination of g, we need to find the maximum and minimum possible values of g based on the uncertainties in L and T.
The maximum possible value of g can be found by using the minimum value of L (19.9cm) and the maximum value of T (90.5 s), which gives g=9.69 m/s^2. The minimum possible value of g can be found by using the maximum value of L (20.1cm) and the minimum value of T (89.5 s), which gives g=10.03 m/s^2.
Therefore, the accuracy in the determination of g is ±0.17 m/s^2, which is the difference between the maximum and minimum possible values of g.
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The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g?
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The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g?.
The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The period of oscillation of a simple pendulum is T=2πL/g−−−−√. Measured value of L is 20.0cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g?.
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