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The formula for the period of a simple pendulum is T is equals to 2 π √l/g such a pendulum is used to determine the fractional error in the measurement of the period t is -x and that in the measurement of the length L is -y the fractional error in the calculated value of g is not the greater than ?
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The formula for the period of a simple pendulum is T is equals to 2 π ...
Calculation of Fractional Error in the Value of g
The period of a simple pendulum is given by the formula:
T = 2π√(l/g)
Where T is the period of the pendulum, l is the length of the pendulum and g is the acceleration due to gravity.
Fractional Error in the Measurement of the Period
If the measured value of the period is t-x, where x is the fractional error, then the actual value of the period is:
T' = T + Tx
Substituting the value of T from the above equation in the formula of the period, we get:
T' = 2π√(l/g + lx)
The fractional error in the calculated value of the period is:
(T' - T)/T = lx/√(l/g)
As x is small, the fractional error in the measurement of the period is negligible.
Fractional Error in the Measurement of the Length
If the measured value of the length is L-y, where y is the fractional error, then the actual value of the length is:
l' = l + Ly
Substituting the value of l from the above equation in the formula of the period, we get:
T' = 2π√((l + Ly)/g)
The fractional error in the calculated value of the period is:
(T' - T)/T = (Ly/2l) + (Ly/2g√((l + Ly)/g))
The maximum value of the fractional error occurs when y = -1/2. Substituting this value in the above equation, we get:
(T' - T)/T ≤ 1/4
Conclusion
Thus, the fractional error in the calculated value of g is not greater than 1/4, even if the fractional errors in the measurement of the period and the length are -x and -y respectively.
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The formula for the period of a simple pendulum is T is equals to 2 π √l/g such a pendulum is used to determine the fractional error in the measurement of the period t is -x and that in the measurement of the length L is -y the fractional error in the calculated value of g is not the greater than ?
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The formula for the period of a simple pendulum is T is equals to 2 π √l/g such a pendulum is used to determine the fractional error in the measurement of the period t is -x and that in the measurement of the length L is -y the fractional error in the calculated value of g is not the greater than ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The formula for the period of a simple pendulum is T is equals to 2 π √l/g such a pendulum is used to determine the fractional error in the measurement of the period t is -x and that in the measurement of the length L is -y the fractional error in the calculated value of g is not the greater than ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The formula for the period of a simple pendulum is T is equals to 2 π √l/g such a pendulum is used to determine the fractional error in the measurement of the period t is -x and that in the measurement of the length L is -y the fractional error in the calculated value of g is not the greater than ?.
The formula for the period of a simple pendulum is T is equals to 2 π √l/g such a pendulum is used to determine the fractional error in the measurement of the period t is -x and that in the measurement of the length L is -y the fractional error in the calculated value of g is not the greater than ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The formula for the period of a simple pendulum is T is equals to 2 π √l/g such a pendulum is used to determine the fractional error in the measurement of the period t is -x and that in the measurement of the length L is -y the fractional error in the calculated value of g is not the greater than ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The formula for the period of a simple pendulum is T is equals to 2 π √l/g such a pendulum is used to determine the fractional error in the measurement of the period t is -x and that in the measurement of the length L is -y the fractional error in the calculated value of g is not the greater than ?.
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