If pressure P,velocity V and time T are taken | vedclass

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(A) Let the force $F$ be expressed as $F = P^{\alpha} V^{\beta} T^{\gamma}$.The dimensional formula for force is $[M^1 L^1 T^{-2}]$.The dimensional fo

Vedclass · Accepted Answer

$P{V^2}{T^2}$

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(A) Let the force $F$ be expressed as $F = P^{\alpha} V^{\beta} T^{\gamma}$.The dimensional formula for force is $[M^1 L^1 T^{-2}]$.The dimensional formula for pressure $P$ is $[M^1 L^{-1} T^{-2}]$.The dimensional formula for velocity $V$ is $[L^1 T^{-1}]$.The dimensional formula for time $T$ is $[T^1]$.Substituting these into the equation:$[M^1 L^1 T^{-2}] = [M^1 L^{-1} T^{-2}]^{\alpha} [L^1 T^{-1}]^{\beta} [T^1]^{\gamma}$$[M^1 L^1 T^{-2}] = [M^{\alpha} L^{-\alpha + \beta} T^{-2\alpha - \beta + \gamma}]$Comparing the powers of $M$,$L$,and $T$ on both sides:For $M$: $\alpha = 1$For $L$: $-\alpha + \beta = 1 \Rightarrow -1 + \beta = 1 \Rightarrow \beta = 2$For $T$: $-2\alpha - \beta + \gamma = -2 \Rightarrow -2(1) - 2 + \gamma = -2 \Rightarrow -4 + \gamma = -2 \Rightarrow \gamma = 2$Thus,the dimensional formula for force is $P^1 V^2 T^2$ or $P V^2 T^2$.

If pressure $P$,velocity $V$ and time $T$ are taken as fundamental physical quantities,the dimensional formula of force is

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