Time period of oscillations of a simple pendulum is given as
T=2√ where l is length of pendulum.
For pendulum A: Given, completes 10 oscillations is 20 s.
Therefore, time period of single oscillation
==2 ⇒TA=2 ⇒2π√=2 → (1)
For pendulum B: Given, completes 8 oscillations in 10 s.
Therefore, time period of single oscillation
== ⇒TB= ⇒2π√= →(2)
Divide Eq. (1) by Eq. (2), we get
= ⇒√= ⇒√= ⇒=()2= Therefore, ratio of lengths of pendulums A and B is