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Application of Dimensional analysis (III)- Check the dimensional correctness - (Concept)

It is based on the principle of homogeneity. According to this principle, both sides of an equation must be the same.

L.H.S = R.H.S

It also states that only those physical quantities can be added or subtracted which have the same dimensions.

If the dimension of each term on both sides is the same, then the equation is dimensionally correct, otherwise not.

A dimensionally correct equation may or may not be physically correct.

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Exam	Chapter
JEE MAIN	Physics and Measurement

A.	M²L²T^-2
B.	MLT^-2
C.	M⁰LT^-4
D.	M²LT^-4

A.	$F=\frac{mV^2}{r^2}$
B.	$S=ut+\frac{1}{2}at^2$
C.	$K.E=\frac{1}{2}mV^2r$
D.	$t=\sqrt{g}$

A.	$\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \theta^{-1}\right]$
B.	$\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]$
C.	$\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$
D.	$\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0}\right]$

A.	$W=\tau \theta$
B.	$\mathrm{v}=\frac{\pi \mathrm{pa}^{4}}{8 \eta \mathrm{L}}$
C.	$\mathrm{h}=\frac{2S \cos \theta}{\operatorname{\rho rg}}$
D.	$J=\epsilon \frac{\partial E}{\partial t}$

A.	$y = A \sin vt$
B.	$y = A \sin (wt-kx)$
C.	$T = 2\pi \sqrt {\frac{l}{g}}$
D.	$F = \frac{mv^2}{r}$

A.	Dimensions of $\beta$ is same as that of force.
B.	Dimensions of $\alpha^{-1}\mathrm{x}$ is same as that of energy.
C.	Dimensions of $\eta^{-1} \sin \theta$ is same as that of $\alpha \beta.$
D.	Dimensions of $\alpha$ is same as that of $\beta.$

A.	$\mathrm{A}=[\mathrm{LT}], \mathrm{B}=\left[\mathrm{L}^{-1} \mathrm{~T}^{-1}\right]$
B.	$\mathrm{A}=\left[\mathrm{L}^{-1} \mathrm{~T}^{-1}\right], \mathrm{B}=[\mathrm{LT}]$
C.	$\mathrm{A}=\left[\mathrm{L}^{-1} \mathrm{~T}\right], \mathrm{B}=\left[\mathrm{LT}^{-1}\right]$
D.	$\mathrm{A}=\left[\mathrm{L}^{-1} \mathrm{~T}^{-1}\right], \mathrm{B}=\left[\mathrm{LT}^{-1}\right]$

A.	$\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}}{\mathrm{GM}^2}$
B.	$\mathrm{T}^2=4 \pi^2 \mathrm{r}^3$
C.	$\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^3}{\mathrm{GM}}$
D.	$\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^2}{G M}$

A.	If both assertion and reason are true and reason is the correct explanation of assertion.
B.	If both assertion and reason are true but reason is not the correct explanation of assertion.
C.	If assertion is true but reason is false.
D.	If both assertion and reason are false.

A.	$\mu_0^{\frac{1}{2}} \varepsilon_0^{\frac{-1}{2}}$
B.	$\mu _{0}^{-\frac{1}{2}}\varepsilon_{0}^ {\frac{1}{2}}$
C.	$\mu_0^{\frac{1}{2}} \varepsilon_0^{\frac{1}{2}}$
D.	$\mu_0^{\frac{-1}{2}} \varepsilon_0^{\frac{-1}{2}}$

A.	$M^{\frac{1}{2}} F^{\frac{1}{2}} L^{\frac{1}{2}}$
B.	$M^{-\frac{1}{2}} F^{-\frac{1}{2}} L^{\frac{1}{2}}$
C.	$M^{\frac{1}{2}} F^{-\frac{1}{2}} L^{\frac{1}{2}}$
D.	$M^{\frac{1}{2}} F^{\frac{1}{2}} L^{-\frac{1}{2}}$

A.	$M L T^{\frac{1}{2}}$
B.	$M L^{\frac{-1}{2}} T^{\frac{1}{2}}$
C.	$M^{\frac{1}{2}} L^{\frac{-1}{2}} T^{\frac{-1}{2}}$
D.	$M L^{\frac{1}{2}} T^{\frac{-1}{2}}$

A.	$\left[R T \varepsilon_0\right]$
B.	$[R T ]$
C.	$\left[R \varepsilon_0\right]$
D.	$\left[ T \varepsilon_0\right]$

A.	$\frac{(P-Q)}{R}$
B.	PQ - R
C.	PQ/R
D.	$\frac{\left(P R-Q^2\right)}{R}$

A.	None
B.	None
C.	None
D.	None

A.	[LT]
B.	[T]
C.	$[T^{-1}]$
D.	$[T^{-2}]$

A.	$RC$
B.	$\frac{L}{R}$
C.	$\sqrt{L C}$
D.	All of these

A.	$F=\frac{m v^2}{r^2}$
B.	$S=u t-\frac{1}{2} a t^2$
C.	$K=\frac{1}{2} \frac{m v^2}{r}$
D.	$t=\sqrt{\frac{2 g}{h}}$

A.	$E^{2}=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^4$
B.	$\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^2$
C.	$\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^2$
D.	$E^2=p^2 c^2+m^2 c^4$

A.	L
B.	$\mathrm{L}^3 \mathrm{~T}^{-2}$
C.	$\mathrm{L}^2 \mathrm{~T}^{-2}$
D.	$\mathrm{L}^2 $

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Application of Dimensional analysis (III)- Check the dimensional correctness - (Concept)

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