The length of a simple pendulum is made one-ninth. Its time period becomes____its initial value.
We have time period of a pendulum T∝√l
∴T1T2=√l1l2 where T1 and T2 are the initial and final time periods of the simple pendulum and l1 and l2 are the initial and final lengths of the pendulum. If the length of the simple pendulum is made one-ninth i.e.,l2=l19
⇒T1T2=√l1l19 ⇒T1T2=√9 ⇒T1T2=3 ⇒T2=13 T1
i.e., the time period of the pendulum becomes one third its initial value.