The pair(s) of physical quantities that have the same dimensions … - Vidyadip

MCQ

The pair$(s)$ of physical quantities that have the same dimensions is $($are$):$

A
Volumetric strain and coefficient of friction.
B
Disintegration constant of a radioactive substance and frequency of light wave.
✓
Heat capacity and gravitational potential.
D
Planck's constant and torque.

✓

Answer

Correct option: C.

Heat capacity and gravitational potential.

Volumetric strain $\frac{\Delta\text{V}}{\text{V}}=\frac{\text{L}^3}{\text{L}^3}=1$
Coefficient of friction $\mu=\frac{\text{F}}{\text{R}}=\frac{\text{MLT}^{-2}}{\text{MLT}^{-2}}=1$
$\lambda=\frac{0.693}{\text{T}}=\text{T}^{-1}$
$\text{v}=\frac{1}{\text{T}}=\text{T}^{-1}$
Both have same dimensions.
Heat capacity is measured in $\text{cal/kg}$ and gravitational potential is measured in $\text{joule/ kg.}$ Both have the same dimensions $\ce{[L^2T^{-2}]}$.

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