Question

The dimensional formula of torque is
\[(A)\left[ {M{L^2}{T^{ - 2}}} \right]\]
\[(B)\left[ {ML{T^{ - 2}}} \right]\]
\[(C)\left[ {M{L^{ - 1}}{T^{ - 2}}} \right]\]
\[(D)\left[ {M{L^{ - 2}}{T^{ - 2}}} \right]\]

Answer 1

Hint: We all know that the dimension formula of any quantity gives a thought about the fundamental quantities that are present within the given physical quantity. Torque is termed as the product of angular acceleration and moment of inertia. We are able to simply calculate the dimensional formula of torque by putting the dimensional formulas of angular acceleration and moment of inertia in the respective equation.

Complete step-by-step solution:
The term force is employed in the linear motions, while torques are employed in the rotational motions, but they’re having an identical basis. Torque is proportional to the lever arm distance. i.e., the distance between the rotation axis and therefore the force applied point. The formula of torque is given by,
Torque = angular acceleration $ \times $ moment of inertia ………….. (1).
The moment of inertia = Mass $ \times $ radius of gyration2
Dimensional formula of the Moment of Inertia \[ = M{L^2}\]
Angular acceleration = Angular velocity $ \times $ time
The dimensional formula of angular acceleration will be, \[ = {T^{ - 2}}\]
On substituting these formulas in equation (1),
The dimensional formula of Torque will be,
\[ = \left[ {{M^1}{L^2}} \right] \times \left[ {{T^{ - 2}}} \right]\]
\[ = \left[ {M{L^2}{T^{ - 2}}} \right]\]
Where \[M\] is the mass, \[L\] is the length, and \[T\] is the time
Hence, option A is correct.
Additional information:
Torque helps us to turn or rotate things. It’s also called a twisting force. There are such a lot of examples of torque in our reality. We will take the instance of tightening the lug nuts on the wheel. It is also most important for the generation of power from the car’s engine. Torque represents the number of loads an engine can handle. This load is employed for the generation of power, which helps within the rotation of the engine about its axis.

Note: When they’re asking for dimensional formulas of any quantity, revise the expression of that quantity and then put the dimensional formulas of substituent quantities in the solution, and develop the final dimensional formula. According to seven fundamental quantities, there are seven fundamental dimensions available.