Question

Dimensional formula of torque is
A. \[ML{T^{ - 2}}\]
B. \[M{L^2}{T^{ - 2}}\]
C. $M{L^2}{T^{ - 3}}$
D. $ML{T^{ - 3}}$

Answer 1

Hint: We know that the dimension formula of any quantity gives an idea about the fundamental quantities that are present in the given physical quantity. For example length is denoted by L and mass is denoted by M etc. along with these there are total seven fundamental dimensions.

Complete step by step answer:
We can define torque in simple terms as the twisting force that causes rotation. It is given by the expression; $\tau = F.r\sin \Theta $ where $\tau $ is torque vector, $F$ is force which causes it and $r$ is length of the momentum arm and $\Theta $ is the angle between force vector and momentum arm. Torque can be of two types: static and dynamic. If the angle between force vector and momentum arm is ${90^o}$ then the sine term will be one and the expression becomes ; $\tau = F.r$. The direction of torque can be determined by right hand grip rule.
The SI unit for torque is Newton- meter as we know that the unit of force is newton which is equal to $Force = mass \times acceleration$. The SI unit of mass is Kilogram and acceleration is $meter/{\sec ^2}$.
Dimension formula of torque = dimension formula of force X dimension formula of length$ \Rightarrow [ML{T^{ - 2}}][L] = [M{L^2}{T^{ - 2}}]$
Hence the dimensional formula of torque is $M{L^2}{T^{ - 2}}$.

Thus option B is the correct answer to this problem.

Note:
We can calculate the dimension formula of any quantity by calculating the fundamental dimension of that quantity. Any dimension formula is expressed in the terms of power of $M,L$ and $T$ where $M$ denotes mass, $L$ denotes length and $T$ denotes time. There are seven fundamental dimensions according to seven fundamental quantities.