A simple pendulum executes S.H.M. in water with a time period `T_(w)`. When the bob executes S.H.M. in air, time period is `T_(a)`, IF the density of bob of simple pendulum is 5000/3 kg/`m^(3)` and frictional force of water is neglected, then find the relation between `T_(w) and T_(a)`.

Explanation

To find the relation between the time periods \( T_w \) (time period in water) and \( T_a \) (time period in air) for a simple pendulum, we need to consider the effective acceleration due to gravity in both mediums.

### Step-by-Step Solution:

1. **Understanding the Time Period Formula**:
The time period \( T \) of a simple pendulum is given by the formula:
\[
T = 2\pi \sqrt{\frac{L}{g_{\text{effective}}}}
...