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.

Answer 1

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