If the percentage error in the measurement of length of a pendulum is 4% and time period of oscillations is2%, then calculate the percentage error in measuring the acceleration due to gravity of that place..
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If the percentage error in the measurement of the length of a pendulum is 4% and the time period of oscillations is 2%, then what is the percentage error in measuring the acceleration due to the gravity of that place?
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The safest way to deal with uncertainties espescially if you have doubts is to work out the maximum and minimum possible values.
Use the formula for the pendulum T=2 pi root(l/g).
Choose a value for ‘l’ eg 1 metre and work out the period T. Take g be to be say 10N/kg
Rearrange the equation to make g the subject. g=4 pi*2 l/T^2
to calculate the maximum value use use length l x1.04 (max value for l) and for the period use your T x 0.98.
Repeat this using l x 0.96 and T x 1.02 - this gives the minimum value for g.
Now you have two values, find the difference and half of this is the +/- iuncertainty that you should be quoting. If you want a percentage use (this uncertainty over your mid range value) x 100.
You can add/ subtract percentage errors but people often lose track of what they are really doing. I suppose it depends upon whether you want a quick answer or an understanding/ feel for what you are calculating.
What is the percentage of error in the measurement of time period of a pendulum if the maximum measure of l and g are 2% and 4%?
The percentage error in the measurement of time and length of a simple pendulum are 0.2% and 2% respectively the maximum % error in L/T^2 will be?
If the length and time period of an oscillating pendulum have an error of 1% and 3%, then what is the error in the measurement of acceleration due to gravity?
The period of oscillation of pendulum is T=2π√L/g. Measured value of L is 20cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90s using a wrist watch of 1s resolution. What is accuracy in determination of g?
The time period of a simple pendulum is 5 seconds. How many oscillations does it complete in 10 seconds?
Thank you for A2A
Time period of a pendulum is given as
T=2πLg−−√
Rearranging in terms of g we get
g=4π2LT2
Using Theory of error where Δg is error in g and so on we get
Δgg×100=(ΔLL×100)+(2×ΔTT×100)
Inserting given values of errors we get
Δgg×100=(4%)+(2×2%)
Percentage error in g=8%
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Formula for time period of simple pendulum is:
T=2πlg−−√
now put l= 4l100
and T=2T100
now we can write, g= (2π)2.lT2
now put the values and find the value of g;
Hope this helps.