What is the dimensional formula for the torque?

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]