(A) According to the principle of dimensional homogeneity,the dimensions of each term added or subtracted in an equation must be the same.In the given

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(A) According to the principle of dimensional homogeneity,the dimensions of each term added or subtracted in an equation must be the same.In the given equation $(P + \frac{a}{V^2}) = \frac{b\theta}{l}$,the term $P$ is added to $\frac{a}{V^2}$.Therefore,$[P] = [\frac{a}{V^2}]$.We know that the dimensional formula for pressure $P$ is $[ML^{-1}T^{-2}]$ and for volume $V$ is $[L^3]$.Thus,$[a] = [P] \times [V^2]$.Substituting the dimensions: $[a] = [ML^{-1}T^{-2}] \times [L^3]^2$.$[a] = [ML^{-1}T^{-2}] \times [L^6]$.$[a] = [ML^5T^{-2}]$.

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

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The equation of state of some gases can be expressed as $(P + \frac{a}{V^2}) = \frac{b\theta}{l}$,where $P$ is the pressure,$V$ is the volume,$\theta$ is the absolute temperature,and $a$ and $b$ are constants. The dimensional formula of $a$ is

AIPMT 1996 All AIPMT

A
$[ML^5T^{-2}]$
B
$[M^{-1}L^5T^2]$
C
$[ML^{-5}T^{-1}]$
D
$[ML^5T^1]$

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Dimensional Analysis, Uses and Limitations

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The equation of state of some gases can be expressed as $(P + \frac{a}{V^2}) = \frac{b\theta}{l}$,where $P$ is the pressure,$V$ is the volume,$\theta$ is the absolute temperature,and $a$ and $b$ are constants. The dimensional formula of $a$ is

Similar Questions

Applying the principle of homogeneity of dimensions,determine which one is correct. Where $T$ is time period,$G$ is gravitational constant,$M$ is mass,and $r$ is the radius of the orbit.

The density of a material in $SI$ units is $128 \ kg \ m^{-3}$. In a system of units where the unit of length is $25 \ cm$ and the unit of mass is $50 \ g$,the numerical value of the density of the material is:

Using dimensional analysis,the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as

Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.

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