Question

Which of the following physical quantity has the dimensions of $[M{L}^2{T}^{-3}]$ ?

• A. pressure
• B. work
• C. impulse
• D. power

Answer 1

Answer: (D)

Dimension of work $(W)=$ force $\times$ distance
$=\left[ML{T}^{-2}\right][L]=\left[M{L}^2{T}^{-2}\right]$,
power $(P)=\frac{\text{ work }}{\text{ time }}=\frac{\left[M{L}^2{T}^{-2}\right]}{[T]}=\left[M{L}^2{T}^3\right];$ pressure
$(p)=\frac{\text{ force }}{\text{ area }}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^2\right]}=\left[M{L}^{-1}{T}^{-2}\right]$
and impulse $=$ force$\times$ time $=\left[ML{T}^{-2}\right][T]=\left[ML{T}^{-1}\right].$
Therefore power has the same dimension as given in the question.