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 $\theta = \frac{l}{r}$ has the unit radian, but its dimensional formula is $[M^{0} L^{0} T^{0}]$.
$(b)$ Strain $= \frac{\Delta l}{l} = \frac{\text{Change in length}}{\text{Original length}}$. It has neither a unit nor dimensions.
$(c)$ Gravitational constant $G = 6.67 \times 10^{-11} \text{ N} \cdot \text{m}^{2} \cdot \text{kg}^{-2}$. It is a constant with a unit.
$(d)$ Reynolds number $(Re)$ is a dimensionless constant.
$(b)$ Strain $= \frac{\Delta l}{l} = \frac{\text{Change in length}}{\text{Original length}}$. It has neither a unit nor dimensions.
$(c)$ Gravitational constant $G = 6.67 \times 10^{-11} \text{ N} \cdot \text{m}^{2} \cdot \text{kg}^{-2}$. It is a constant with a unit.
$(d)$ Reynolds number $(Re)$ is a dimensionless constant.
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Similar Questions
If $e$ is the charge,$V$ is the potential difference,and $T$ is the temperature,then the units of $\frac{eV}{T}$ are the same as that of:
Easy
View SolutionMatch List $I$ with List $II$:
List $I$ List $II$ $(A)$ Young's Modulus $(Y)$ $(I)$ $[M L^{-1} T^{-1}]$ $(B)$ Co-efficient of Viscosity $(\eta)$ $(II)$ $[M L^2 T^{-1}]$ $(C)$ Planck's Constant $(h)$ $(III)$ $[M L^{-1} T^{-2}]$ $(D)$ Work Function $(\phi)$ $(IV)$ $[M L^2 T^{-2}]$
Choose the correct answer from the options given below:
| List $I$ | List $II$ |
| $(A)$ Young's Modulus $(Y)$ | $(I)$ $[M L^{-1} T^{-1}]$ |
| $(B)$ Co-efficient of Viscosity $(\eta)$ | $(II)$ $[M L^2 T^{-1}]$ |
| $(C)$ Planck's Constant $(h)$ | $(III)$ $[M L^{-1} T^{-2}]$ |
| $(D)$ Work Function $(\phi)$ | $(IV)$ $[M L^2 T^{-2}]$ |
Choose the correct answer from the options given below:
Identify the pair of physical quantities which have different dimensions.
Which of the following groups has different dimensions?
MediumIIT 2005
View SolutionMatch the List-$I$ with List-$II$:
List-$I$ List-$II$ $A$. Spring constant $I$. $ML^2 T^{-2} K^{-1}$ $B$. Thermal conductivity $II$. $ML^0 T^{-2}$ $C$. Boltzmann constant $III$. $ML^2 T^{-3} A^{-2}$ $D$. Inductive reactance $IV$. $MLT^{-3} K^{-1}$
Choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| $A$. Spring constant | $I$. $ML^2 T^{-2} K^{-1}$ |
| $B$. Thermal conductivity | $II$. $ML^0 T^{-2}$ |
| $C$. Boltzmann constant | $III$. $ML^2 T^{-3} A^{-2}$ |
| $D$. Inductive reactance | $IV$. $MLT^{-3} K^{-1}$ |
Choose the correct answer from the options given below:
DifficultJEE MAIN 2026
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