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The period of oscillation of a simple pe...

The period of oscillation of a simple pendulum is `T = 2pisqrt(L/g).` Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is :

A

`2%`

B

`3%`

C

`1%`

D

`5%`

Text Solution

Verified by Experts

Given `(Delta)/(L) = (0.1)/(20)`
`T = (90)/(100) sec DeltaT = (1)/(100)sec`
`(DeltaT)/(T) = (1)/(90)`
`g = ((1)/(4pi^(2))) (L)/(T^(2)) rArr (Deltag)/(g) xx 100 % = (DeltaL)/(L) xx 100 + (2DeltaT)/(T) xx 100`
`(Deltag)/(g)xx100%=((0.1)/(20))100+2((1)/(90))100=2.72%`
so nearest option is `3%` .
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