Hello,

To determine the dimensions of W in the given equation. We know that W represents work done, which has dimensions of energy. The equation W = KT^2/2 involves the displacement x, Boltzmann constant k, and temperature T.

The dimensions of displacement x are [L], the dimensions of the Boltzmann constant k are [M L^2 T^-2 K^-1], and the dimensions of temperature T are [T].

By substituting the dimensions into the equation, we get [L] = [M L^2 T^-2 K^-1] * [T]^2 / 2. Simplifying this, we find that the dimensions of W are [M L^2 T^-2].

So, the correct option is d. [M L^2 T^-2].

Hope this helps,

Thank you