$$T_0$$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $$\frac{1}{16}$$ times of its initial value, the modified time period is

The time period of a simple pendulum is given by: $$T = 2\pi\sqrt{\frac{L}{g}}$$

Initially, the time period is $$T_0 = 2\pi\sqrt{\frac{L}{g}}$$.

When the length is reduced to $$\frac{1}{16}$$ of its original value, the new length is $$L' = \frac{L}{16}$$.

The new time period is: $$T' = 2\pi\sqrt{\frac{L'}{g}} = 2\pi\sqrt{\frac{L/16}{g}} = 2\pi\sqrt{\frac{L}{16g}} = \frac{1}{4} \cdot 2\pi\sqrt{\frac{L}{g}} = \frac{T_0}{4}$$

Therefore, the modified time period is $$\frac{T_0}{4}$$.