Chapter 13 - Vibrations and Waves - Learning Path Questions and Exercises - Conceptual Questions - Page 483: 7

The period of oscillation is increased by $\sqrt 2$

If the length of the pendulum is $l_{1}$, its period is $T_{1}=2\times pi\times \sqrt \frac{l_{1}}{g}$ If length is doubled, that is $l_{2}=2l_{1}$, then new period is $T_{2}=2\times pi\times \sqrt \frac{2l_{1}}{g}=\sqrt 2T_{1}$ Hence, the period of oscillation is increased by $\sqrt 2$