A sphere of radius ` 0.1m` and mass `8 pi kg` is attached to the lower end of a steel wire of length `5.0 m` and diameter `10^(-3)`. The wire is suspended from `5.22 m` high ceiling of a room . When the sphere is made to swing as a simple pendulum, it just grazes the floor at its lowest point. Calculate the velocity of the sphere at the lowest position . Young's modulus of steel is `(1.994xx10^(11) N//m^(2))`.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the total length of the pendulum
The total length of the pendulum when the sphere is at its lowest point is the length of the wire plus the radius of the sphere.

\[ L_{\text{total}} = L_{\text{wire}} + r_{\text{sphere}} = 5.0 \, \text{m} + 0.1 \, \text{m} = 5.1 \, \text{m} \]
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