To be dimensionally consistent, force $\left[M L / \mathrm{T}^{2}\right]$, pressure $\left[\mathrm{M}^{\mathrm{L}} \mathrm{LT}^{2}\right]$, and length $[\mathrm{L}]$ must be related as follows.
A) force $=$ pressure $\times$ length 2
B) force $=$ pressure $2 \times$ length 2
C) force $=$ pressure $\times$ length
D) force $=$ pressure $^{2} \times$ length

Question

Quizplus · Accepted Answer

CForce has dimensions $[MLT^{-2}]$. Pressure has dimensions $[ML^{-1}T^{-2}]$, and length has dimensions $[L]$. Multiplying pressure by length $[ML^{-1}T^{-2} \times L]$ gives the dimensions of force $[MLT^{-2}]$, which matches option A and C. Option A is a misprint and should likely represent force = pressure $\times$ length^2, which would not be dimensionally consistent, making C the correct interpretation.

To Be Dimensionally Consistent, Force [ML/T2]\left[M L / \mathrm{T}^{2}\right][ML/T2] , Pressure [MLLT2]\left[\mathrm{M}^{\mathrm{L}} \mathrm{LT}^{2}\right][MLLT2]

To Be Dimensionally Consistent, Force $\left[M L / \mathrm{T}^{2}\right]$ , Pressure $\left[\mathrm{M}^{\mathrm{L}} \mathrm{LT}^{2}\right]$