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In a sample pendulum experiment, length ...

In a sample pendulum experiment, length is measured as `31.4cm` with an accuracy of `1mm`. The time for `100` ocscillations of pendulum is `112s` with an accuracy of `0.01s`. The percentage accuracy in `g` is

A

`4.6%`

B

`2.3%`

C

`9%`

D

`10%`

Text Solution

Verified by Experts

The correct Answer is:
B
`l=3.14 cm and Deltal=1mm=0.1cm," "T=(112.0)/(100)=1.12s and DeltaT=0.01s`
Formula for g is `g=4pi^(2)((l)/(T^(2)))," "(Deltag)/(g)=((Deltal)/(l))+2((DeltaT)/(T))`
`=((0.1)/(31.4))+2((0.01)/(1.12))=0.003+0.02=0.023`
Relative error in determining g is 0.23 and percentage error `=0.023xx100=2.3%`
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