Question

 The dimensions of torque are:
A. $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{3}}}{{\text{T}}^{\text{-3}}}]$
B. $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{-1}}}{{\text{T}}^{\text{-1}}}]$
C. $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}]$
D. $\text{ }\!\![\!\!\text{ M}{{\text{T}}^{\text{-2}}}]$

Answer 1

Hint: The dimensions of torque depends upon the quantities signified by torque. To find the dimension of torque, we are required to know the definition and the unit of torque.

Complete step by step answer:
 Torque is the rotational equivalent of linear force. Torque can also be referred to as the moment, moment of force, rotational force or even the turning effect, depending on the field of study.
In case of torque there will be one or both of the angular velocity or the moment of inertia of an object will be changing.
The unit of torque will be newton metre. By newton, we mean the unit of force.
As we know force = $\text{mass }\!\!\times\!\!\text{ acceleration}$
The dimension of force is $\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-2}}}]$. Here M signifies the dimension of mass. The dimension of acceleration is $\text{ }\!\![\!\!\text{ L}{{\text{T}}^{\text{-2}}}]$. Acceleration is defined as the rate of change of velocity with time. The unit of acceleration is meters per second square.
So, the unit of torque is $\text{newton }\!\!\times\!\!\text{ metre}$.
Or, we can say $\text{mass }\!\!\times\!\!\text{ acceleration }\!\!\times\!\!\text{ metre}$.
So the dimension of torque is $\left[ \text{M} \right]\text{ }\times \text{ }\left[ \text{L}{{\text{T}}^{\text{-2}}} \right]\text{ }\times \text{ }\left[ \text{L} \right]$
This can also be written by $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}]$.
So, the dimension of torque is $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}]$. Therefore, the correct answer is Option C.
Note: Torque helps us to turn or rotate things. It is also known as twisting force. There are so many examples of torque in our real life. We can take the instance of tightening the lug nuts on the wheel. Torque is also very important for the generation of power from the car’s engine. Torque represents the amount of load an engine can handle. This load is used for the generation of power, which helps in the rotation of the engine about its axis.