Answer
The work done by the weightlifter is zero.
Work Step by Step
By definition, the work is only done when an object changes its position after a force acts on it.
The weightlifter is just holding a barbell above his head. Due to this, the weightlifter’s body is just shaking but not moving from his position.
So, there is no displacement done by the weightlifter.
Since the displacement of the object is zero, therefore, the work done by the weightlifter is also zero.
Example:
Assume that a weightlifter is holding a barbell of $100\text{Kg}$ on his head.
The force acting on the barbell is ${{\mathbf{F}}_{\mathbf{b}}}$.
So,
$\begin{align}
& {{\mathbf{F}}_{\mathbf{b}}}=\text{mg} \\
& \text{=100 Kg}\times \text{9}\text{.8 m}{{\text{s}}^{\text{-2}}} \\
& =980\text{ N}
\end{align}$
Since there is no displacement, thus the displacement is zero.
Now work done by the weightlifter is:
$\begin{align}
& \text{W}=\mathbf{F}\cdot \mathbf{S} \\
& =980\text{ N}\times 0 \\
& =0
\end{align}$
