Dimensions of potential energy are

The correct option is ML²T⁻².

To find the dimensions of potential energy, we can analyze its relationship with work and other mechanical quantities. Potential energy is a form of energy, and all forms of energy (including kinetic energy and work) share the same dimensions.

The relationship between work, force, and displacement is given by:
$\text{Work Done}=\text{Force}\times \text{Displacement}$

To find the dimensions of force, we use Newton's second law:
$\text{Force}=\text{Mass}\times \text{Acceleration}$

Now, let's write down the fundamental dimensions of these basic physical quantities:
• Mass has the dimension $\left[\text{M}\right]$.
• Displacement (which is a length) has the dimension $\left[\text{L}\right]$.
• Acceleration (velocity divided by time) has the dimensions of length divided by time squared:
$\left[\text{Acceleration}\right]=L{T}^{-2}$

Using these fundamental dimensions, we calculate the dimensions of force:
$\left[\text{Force}\right]=M\times L{T}^{-2}=ML{T}^{-2}$

Finally, we multiply the dimensions of force by the dimension of displacement (length) to get the dimensions of potential energy:
$\left[\text{Potential Energy}\right]=\left[\text{Force}\right]\times \left[\text{Displacement}\right]$

Substituting the values:
$\left[\text{Potential Energy}\right]=\left(ML{T}^{-2}\right)\times L=M{L}^2{T}^{-2}$

Therefore, the dimensions of potential energy are ML²T⁻².