Identify the pair whose dimensions are equal

The correct option is Torque and work.

To identify the pair whose dimensions are equal, we can determine the dimensional formula for each quantity mentioned in the options.

1. Torque:
Torque ($\tau$) is defined as the product of force and the perpendicular distance from the axis of rotation.
$\tau =\text{Force}\times \text{Distance}$
The dimensional formula for force is:
$\left[\text{Force}\right]=\left[{\text{MLT}}^{-2}\right]$
The dimensional formula for distance is:
$\left[\text{Distance}\right]=\left[\text{L}\right]$
Therefore, the dimensional formula for torque is:
$\left[\tau \right]=\left[{\text{MLT}}^{-2}\right]\times \left[\text{L}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$

2. Work:
Work ($W$) is defined as the product of force and displacement in the direction of the force.
$W=\text{Force}\times \text{Displacement}$
The dimensional formula for displacement is:
$\left[\text{Displacement}\right]=\left[\text{L}\right]$
Therefore, the dimensional formula for work is:
$\left[W\right]=\left[{\text{MLT}}^{-2}\right]\times \left[\text{L}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$

Since both torque and work have the dimensional formula $\left[{\text{ML}}^2{\text{T}}^{-2}\right]$, their dimensions are equal.

For completeness, let's verify the other options:
- Stress is force per unit area, so its dimensional formula is $\left[{\text{ML}}^{-1}{\text{T}}^{-2}\right]$, which is different from Energy ($\left[{\text{ML}}^2{\text{T}}^{-2}\right]$).
- Force ($\left[{\text{MLT}}^{-2}\right]$) has different dimensions compared to both Stress and Work.