Question

a simple pendulum is executing simple harmonic motion with a time T if the length of a pendulum is increased by 21% find the increase in its time period. ​

Answer 1

Hey

Initial time period of simple pendulum, T₁ = T

Initial length of the pendulum, I₁ = 100 I

Final length of the pendulum, I₂ = 121 I

  Time period of simple pendulum,

                           T = 2π√I/g

=>                       T ∝ √I

Hence,                 T₂/T₁ = √I₂/I₁ = √121/100

                  = 1.1

∴ Increase in time period

                            = 1.1 T₁ - T₁ = 0.1 T₁

FINAL RESULT = 10 %

GOOD LUCK !