Question

The dimensions of torque are:

• A. [M\(^0\)L\(^3\)T\(^{-2}\)]
• B. [ML\(^3\)T\(^{-1}\)]
• C. [M\(^{-1}\)L\(^{-3}\)T\(^2\)]
• D. [ML\(^2\)T\(^{-2}\)]
• E. [M\(^0\)T\(^0\)T\(^{-1}\)]

Hint:

Torque has the same dimensional formula as energy but represents rotational force rather than work done.

Answer 1

The Correct Option is D

Torque (\( \tau \)) is defined as the cross product of the force (\( F \)) and the lever arm (\( r \)): \[ \tau = r \times F \] The dimensional formula of force (\( F \)) is obtained from Newton’s second law: \[ F = ma \Rightarrow [MLT^{-2}] \] The lever arm (\( r \)) represents distance and has the dimensional formula: \[ [L] \] Multiplying these together: \[ \tau = [L] \times [MLT^{-2}] = [ML^2T^{-2}] \] Thus, the dimensional formula of torque is [ML\(^2\)T\(^{-2}\)].