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Question
When the length of a simple pendulum is decreased by 20 cm, the period changes by 10%. Find the original length of the pendulum.
Solution
L2 = L1 - 0.20
T2 = T1 - 10%T1
`T=2pisqrt(l/g)`
`:.TpropsqrtL`
`:.T_1/T_2=sqrt(L_1/L_2)`
`T_1/(0.9T_1)=sqrt(L_1/(L_1-0.2))`
Squaring both side
`1/0.81=L_1/(L_1-0.2)`
L1-0.2=0.81L1
∴L1-0.81L1=0.2
0.19L1 = 0.2
`L_1=0.20/0.19`
L1=1.053m
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