Torque = Force x Perpendicular distance. Its dimensional formula is [M1L2T-2]
Explanation
Torque is the measure of the force that can cause an object to rotate about an axis. It can be defined as the rotational equivalent of linear force. The point where the object rotates is called the axis of rotation.
Formula
Torque (T) = Moment of Inertia × Angular Acceleration
Dimensional formula of torque
We know that Moment of Inertia (M.O.I) = Radius of Gyration2 × Mass
The dimensional formula of Moment of Inertia = M1 L2 T0 ——(i)
And, Angular Acceleration = Angular velocity × Time-1
∴ The dimensional formula of Angular Acceleration = M0 L0 T-2———(ii)
On substituting equation (i) and (ii) in the formula of torque we get,
Torque = Moment of Inertia × Angular Acceleration
Or, I = [M1 L2 T0] × [M0 L0 T-2] = [M L2 T-2]
Answer
The dimensional formula of torque is [M1L2T-2]