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(D) The dimensions of the given pairs are as follows:$(a)$ Work and energy both have dimensions $[M L^2 T^{-2}]$.$(b)$ Angle (arc/radius) and strain (

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Planck constant and energy

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(D) The dimensions of the given pairs are as follows:$(a)$ Work and energy both have dimensions $[M L^2 T^{-2}]$.$(b)$ Angle (arc/radius) and strain (change in length/original length) are both dimensionless quantities,i.e.,$[M^0 L^0 T^0]$.$(c)$ Relative density (density of substance/density of water) and refractive index (speed of light in vacuum/speed of light in medium) are both ratios of similar physical quantities,hence they are dimensionless,i.e.,$[M^0 L^0 T^0]$.$(d)$ Planck constant $(h)$ has dimensions $[M L^2 T^{-1}]$,while energy $(E)$ has dimensions $[M L^2 T^{-2}]$.Since their dimensions are different,option $(d)$ is the correct answer.

Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

Which one of the following does not have the same dimensions?

Similar Questions

Let $[{\varepsilon _0}]$ denote the dimensional formula of the permittivity of free space and $[{\mu _0}]$ denote the dimensional formula of the permeability of free space. If $M = \text{mass}$,$L = \text{length}$,$T = \text{time}$,and $I = \text{electric current}$,then:

The dimensions of $(\mu_0 \varepsilon_0)^{-1/2}$ are

Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$

The dimensional formula for latent heat is

$MLT^{-1}$ represents the dimensional formula of

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