The physical quantities not having same dimensions are

Option 1)

torque and work

Option 2)

momentum and Planck's constant

Option 3)

stress and Young's modulus

Option 4)

speed and \left ( \mu _{0}\varepsilon _{0} \right )^{-1/2}.

Answers (2)

As we learnt in the concept:

Permeability of free space -

Dimension of permeablity of free space (\mu_{o})-M^{1}L^{1}T^{-2}A^{-2} 

- wherein

\frac{newton}{ampere^{2}},\frac{henry}{metre}

 

and

 

Plank's Constant (h) -

M^{1}L^{2}T^{-1}

- wherein

Joule-sec

 


Option 1)

torque and work

Torque =\vec{r}\times \vec{F}

\left [ Torque \right ]= \left [ ML^{2} T^{-2}\right ]

work = \vec{F}\cdot \vec{r}

\Rightarrow Dimension of work = \left [ ML^{2}T^{-2} \right ]

Both Torque and work have same dimension.

Option 2)

momentum and Planck's constant

Dimension of momentum = \left [ MLT^{-1} \right ]

Dimension of Plank Constant = \left [ P \right ]\left [ \lambda \right ]

= \left [ ML^{2} T^{-1}\right ]

Hence these two have different dimensions.

Option 3)

stress and Young's modulus

Stress = \frac{F}{A}

Young modulus = \frac{Stress}{Strain}

Since strain is dimension less.

hence young modulus have dimension same as stress.

Option 4)

speed and \left ( \mu _{0}\varepsilon _{0} \right )^{-1/2}.

Speed of light = \frac{1}{\sqrt {\mu \epsilon _{0}}}

Hence two have same dimensions.

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