Question

If the length of the simple pendulum is increased by 44%, then what is the change in time period of pendulum [MH CET 2004; UPSEAT 2005]
A) 22% B) 20% C) 33% D) 44%

Answer 1

Let intial length of pendulum is L
Then, time period , $\bold{T=2\pi\sqrt{\frac{L}{g}}}$
Here g is acceleration due to gravity .

Now, length of pendulum is increased by 44%
∴New length of pendulum = L + L × 44/100 = 1.44L
Now, new time period , $\bold{T'=2\pi\sqrt{\frac{1.44L}{g}}}$
⇒$\bold{T'=(1.2)2\pi\sqrt{\frac{L}{g}}}$
⇒$\bold{T'=(1.2)T}$

∴ % change in time period = $\bold{\frac{T'-T}{T}\times100}$
= (1.2T - T)/T × 100
= 0.2 × 100
= 20%

Hence, option (b) is correct