Question

If pressure $P$, Velocity $V$, and time $T$ are taken as fundamental physical quantities, then the dimensional formula for force is:

• A. ${PV}^2{T}^2$
• B. $P^{-1}{V}^2{T}^{-1}$
• C. $PV{T}^2$
• D. $P^{-1}V{T}^2$

Answer 1

Answer: (A)

${PV}^2{T}^2$

$Force=P^{\alpha }{V}^{\beta }{T}^y$

$\Rightarrow ML{T}^{-2}=\left(M{L}^{-1}{T}^{-2}{)}^{\alpha }\right(L{T}^{-1}\left)\beta \right(T{)}^{\gamma }$
$M^1{L}^1{T}^{-2}=M^{\alpha }{K}^{-\alpha +\beta }{T}^{-2\alpha -\beta +\gamma }$
$\alpha =1$
$-\alpha +\beta =1$ $\Rightarrow \beta =2$
$-2\alpha -\beta +\gamma =-2$

$\Rightarrow -2-2+\gamma =-2$

$\Rightarrow force=P{V}^2{T}^2$