# When the Length of a Simple Pendulum is Decreased by 20 Cm, the Period Changes by 10%. Find the Original Length of the Pendulum. - Physics

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

Concept: Some Systems Executing Simple Harmonic Motion
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