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Question

The period of oscillation of a simple pendulum is T=2πLg. Measure 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 a wrist watch of 1 s resolution. The accuracy in the determination of g?


A
2.5%
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B
2.7%
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C
2%
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D
3%
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Solution

The correct option is (A) 2.7%



Step 1, Given data

Time period T=2πLg

L = 20 cm

Step 2, Finding the accuracy

We know,

Time period is

T=2πLg

Squaring on both sides and rearranging,

g=4π2LT2


Now, Δgg=ΔLL+2ΔTT
Putting values
Δgg=1030.2+2×190

Δgg×100=12+209=2.7%

Hence the accuracy in the determination of g is 2.7 %

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