Give an example of
$(a)$ a physical quantity which has a unit but no dimensions
$(b)$ a physical quantity which has neither unit nor dimensions
$(c)$ a constant which has a unit
$(d)$ a constant which has no unit
$(a)$ a physical quantity which has a unit but no dimensions
$(b)$ a physical quantity which has neither unit nor dimensions
$(c)$ a constant which has a unit
$(d)$ a constant which has no unit
$(a)$ Plane angle $\theta=\frac{l}{r}$ radian its unit is radian but $[\theta]=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}$
$(b) $Strain $=\frac{\Delta l}{l}=\frac{\text { Change in length }}{\text { original length }}$
It has neither unit nor dimensions
$(c)$ Gravitational constant
$(\mathrm{G})=6.67 \times 10^{-11} \frac{\mathrm{N} \cdot \mathrm{m}^{2}}{\mathrm{~kg}^{2}}$
$(d)$ Reynold's number is a constant which has no unit.
$(b) $Strain $=\frac{\Delta l}{l}=\frac{\text { Change in length }}{\text { original length }}$
It has neither unit nor dimensions
$(c)$ Gravitational constant
$(\mathrm{G})=6.67 \times 10^{-11} \frac{\mathrm{N} \cdot \mathrm{m}^{2}}{\mathrm{~kg}^{2}}$
$(d)$ Reynold's number is a constant which has no unit.
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- [AIEEE 2008]
Given below are two statements :
$Statement$ $(I)$ : Planck's constant and angular momentum have same dimensions.
$Statement$ $(II)$ : Linear momentum and moment of force have same dimensions.
In the light of the above statements, choose the correct answer from the options given below :
$Statement$ $(I)$ : Planck's constant and angular momentum have same dimensions.
$Statement$ $(II)$ : Linear momentum and moment of force have same dimensions.
In the light of the above statements, choose the correct answer from the options given below :
- [JEE MAIN 2024]