Question

Suppose mass, velocity & time were fundamental physical quantities then find the dimensional formula of pressure.

• A. $\left[ M ^{1} V ^{-1} T ^{-2}\right]$
• B. $[ M ^{1} V ^{-1} T ^{-3} ]$
• C. $\left[ M ^{1} V ^{-2} T ^{-3}\right]$
• D. $\left[M^{2} V^{-2} T^{-3}\right]$

Answer 1

Answer: (B)

$[ P ]= M ^{ x } V ^{ y } T ^{z}$
$\frac{ MLT ^{-2}}{ L ^{2}}= M ^{ x }\left(\frac{ L }{ T }\right)^{ y } T ^{ z }$
$M L^{-1} T^{-2}=M^{x} L^{ Y}T^{z-y}$
$\Rightarrow x=1, \quad y=-1$
$z-y=-2$
$\Rightarrow z=-2+y=-3$