The dimension of torque is

Correct Option: [ML²T⁻²]

To find the dimensional formula of torque, we can use its defining physical relationship: torque is the product of force and perpendicular distance.

$\text{Torque}=\text{Force}\times \text{Distance}$

First, let's determine the dimensions of each component on the right-hand side:

1. Force: According to Newton's second law of motion, force is mass times acceleration.
Dimension of mass = [M]
Dimension of acceleration = [LT^-2]
Therefore, the dimensional formula for force is:
$\left[\text{Force}\right]=\left[{\text{MLT}}^{-2}\right]$

2. Distance: Distance represents length.
Therefore, the dimensional formula for distance is:
$\left[\text{Distance}\right]=\left[\text{L}\right]$

Now, substituting these dimensions back into the torque equation:
$\left[\text{Torque}\right]=\left[{\text{MLT}}^{-2}\right]\times \left[\text{L}\right]$

Multiplying the dimensional terms together:
$\left[\text{Torque}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$

Thus, the dimensional formula of torque is indeed [ML²T⁻²].