Question

The dimensional formula of torque is

• A. $[ML^2T^{-2}]$
• B. $[MLT^{-2}]$
• C. $[ML^{-1}T^{-2}]$
• D. $[ML^{-2}T^{-2}]$

Answer 1

The Correct Option is A

To determine the dimensional formula of torque, we need to understand what torque is and how it is calculated in physics. Torque (\(\tau\)) is defined as the rotational equivalent of linear force. It is the product of force and the perpendicular distance from the axis of rotation to the line of action of the force.

The formula for torque is given by:

\(\tau = r \times F\)

where:

• \(r\) is the perpendicular distance (radius), which has the dimensional formula of length \([L]\).
• \(F\) is the force, which has the dimensional formula \([MLT^{-2}]\) (derived from Newton's Second Law: \(F = ma\), where \(m\) is mass \([M]\) and \(a\) is acceleration \([LT^{-2}]\)).

Applying these dimensions into the formula for torque, we get:

\(\text{Dimensional formula of } \tau = [L] \times [MLT^{-2}] = [ML^2T^{-2}]\)

Therefore, the correct dimensional formula for torque is \([ML^2T^{-2}]\).

Let us now justify why the other options are not correct:

• \([MLT^{-2}]\) is the dimensional formula for force, not torque.
• \([ML^{-1}T^{-2}]\) does not correspond to torque or any standard mechanical quantity related to force or angular displacement.
• \([ML^{-2}T^{-2}]\) similarly does not represent the concept of torque, as torque involves squared length dimensions.

Thus, the correct choice is the first option: [ML^2T^{-2}]