(C) The given expression is $Q V = k P T L^\alpha$.The dimensions of the physical quantities are:$[Q] = M L^{-1} T^{-1}$$[V] = L^3$$[P] = M L^{-1} T^{

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(C) The given expression is $Q V = k P T L^\alpha$.The dimensions of the physical quantities are:$[Q] = M L^{-1} T^{-1}$$[V] = L^3$$[P] = M L^{-1} T^{-2}$$[T] = T$$[L] = L$$k$ is a dimensionless constant, so $[k] = 1$.Equating the dimensions on both sides:$[Q][V] = [k][P][T][L]^\alpha$$(M L^{-1} T^{-1})(L^3) = (1)(M L^{-1} T^{-2})(T)(L^\alpha)$$M L^2 T^{-1} = M L^{-1+\alpha} T^{-1}$Comparing the powers of $L$ on both sides:$2 = -1 + \alpha$$\alpha = 3$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

Medium

Consider an expression $Q V = k P T L^\alpha$ where $V, P, T, L$ are volume, pressure, time, and length respectively. The quantity $[Q]$ has dimension $M L^{-1} T^{-1}$. $k$ is a dimensionless constant. The value of the integer $\alpha$ is:

TS EAMCET 2021 All TS EAMCET

A
$2$
B
$-2$
C
$3$
D
$-1$

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Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

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Consider an expression $Q V = k P T L^\alpha$ where $V, P, T, L$ are volume, pressure, time, and length respectively. The quantity $[Q]$ has dimension $M L^{-1} T^{-1}$. $k$ is a dimensionless constant. The value of the integer $\alpha$ is:

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