(C) The dimension of $\tan \theta$ is $[M^0 L^0 T^0]$ as it is a dimensionless quantity.For the right-hand side,the dimensions are: $[r] = [L]$,$[g] =

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(C) The dimension of $\tan \theta$ is $[M^0 L^0 T^0]$ as it is a dimensionless quantity.For the right-hand side,the dimensions are: $[r] = [L]$,$[g] = [L T^{-2}]$,and $[v^2] = [L^2 T^{-2}]$.Thus,the dimension of $\frac{rg}{v^2}$ is $\frac{[L] [L T^{-2}]}{[L^2 T^{-2}]} = [M^0 L^0 T^0]$.Since both sides have the same dimensions,the equation is dimensionally correct.However,the correct physical formula for the angle of banking is $\tan \theta = \frac{v^2}{rg}$.Therefore,the given equation is numerically incorrect.

Class 11 Physics Units and Measurements Dimensional Analysis, Uses and Limitations

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From the equation $\tan \theta = \frac{rg}{v^2}$,one can obtain the angle of banking $\theta$ for a cyclist taking a curve (the symbols have their usual meanings). Then say,it is

A
Both dimensionally and numerically correct
B
Neither numerically nor dimensionally correct
C
Dimensionally correct only
D
Numerically correct only

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Dimensional Analysis, Uses and Limitations

If electronic charge $e$,electron mass $m$,speed of light in vacuum $c$,and Planck's constant $h$ are taken as fundamental quantities,the permeability of vacuum $\mu_0$ can be expressed in units of

DifficultJEE MAIN 2015

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$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. We know that the equation $AD = C \ln(BD)$ holds true. Which of the following combinations is not a meaningful quantity?

DifficultJEE MAIN 2016

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The speed of a wave produced in water is given by $v = \lambda^a g^b \rho^c$. Where $\lambda$,$g$,and $\rho$ are the wavelength of the wave,acceleration due to gravity,and density of water,respectively. The values of $a$,$b$,and $c$ are,respectively:

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In the relation $y = a \cos (\omega t - kx)$,the dimensional formula for $k$ is

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Given a charge $q$,current $I$ and permeability of vacuum $\mu_0$. Which of the following quantity has the dimension of momentum?

MediumJEE MAIN 2025

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From the equation $\tan \theta = \frac{rg}{v^2}$,one can obtain the angle of banking $\theta$ for a cyclist taking a curve (the symbols have their usual meanings). Then say,it is

Similar Questions

If electronic charge $e$,electron mass $m$,speed of light in vacuum $c$,and Planck's constant $h$ are taken as fundamental quantities,the permeability of vacuum $\mu_0$ can be expressed in units of

$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. We know that the equation $AD = C \ln(BD)$ holds true. Which of the following combinations is not a meaningful quantity?

The speed of a wave produced in water is given by $v = \lambda^a g^b \rho^c$. Where $\lambda$,$g$,and $\rho$ are the wavelength of the wave,acceleration due to gravity,and density of water,respectively. The values of $a$,$b$,and $c$ are,respectively:

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