Question

The dimensions of torque are same as that of

• A. moment of force
• B. pressure
• C. acceleration
• D. impulse

Answer 1

Answer: (A)

Torque is expressed as,
$\tau =$ force $(F)\times$ perpendicular distance $(r)$
So, $[\tau ]=[F]\times [r]=\left[ML{T}^{-2}\right][L]$
$=\left[M{L}^2{T}^{-2}\right]$
Now, the dimension of moment of force $+$ force $\times$ distance
$=\left[ML{T}^{-2}\right]\times \left[L^1\right]=\left[M{L}^2{T}^{-2}\right].$
(b) Dimension of pressure $=$ Force $\times [\text{ Area }{]}^{-2}$
$=\left[ML{T}^{-2}\right]\times \left[L^{-2}\right]=\left[M{L}^{-1}{T}^{-2}\right]$
(c) Dimension of acceleration $=\left[M^0{L}^1{T}^{-2}\right]$
(d) Dimension of impulse $=$ [Force] $x$ [time]
$=\left[ML{T}^{-2}\right]\left[T^1\right]=ML{T}^{-1}$
As, the torque has dimension $\left[M{L}^2{T}^{-2}\right],$
which is correctly matched by the dimensions of moment of force.
So, option (a) is correct.