Question

Consider that \(M\), \(L\), and \(T\) indicate mass, length and time, respectively. If \([ML^2T^{-n}]\) is the dimensional formula for the physical quantity Torque, then the value of \(n\) is _ _ _. (in integer)

Hint:

Torque has the same dimensions as work and energy: \[ ML^2T^{-2} \] but torque is a vector quantity while work is scalar.

Answer 1

Correct Answer: 2

Step 1: Define torque.
Torque is force times the perpendicular distance from the axis, so its dimensions come from force times length.

Step 2: Dimensions of force.
From $F = ma$, force has dimensions $[MLT^{-2}]$.

Step 3: Build torque dimensions.
Multiplying by length, \[ [\tau] = MLT^{-2}\cdot L = ML^2T^{-2} \]

Step 4: Compare with the given form.
The given formula is $ML^2T^{-n}$. Matching the time power gives $n = 2$.

Step 5: Answer.
\[ \boxed{2} \]