Planck's constant $h$, speed of light $c$ and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are)
$(A)$ $M \propto \sqrt{ c }$ $(B)$ $M \propto \sqrt{ G }$ $(C)$ $L \propto \sqrt{ h }$ $(D)$ $L \propto \sqrt{G}$
Planck's constant $h$, speed of light $c$ and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are)
$(A)$ $M \propto \sqrt{ c }$ $(B)$ $M \propto \sqrt{ G }$ $(C)$ $L \propto \sqrt{ h }$ $(D)$ $L \propto \sqrt{G}$
- [IIT 2015]
- A
$(A,B,C)$
- B
$(A,B,D)$
- C
$(A,C,D)$
- D
$(B,C,D)$
Similar Questions
Match List $I$ with List $II$
List $I$
List $II$
$(A)$ Young's Modulus $(Y)$
$(I)$ $\left[ M L ^{-1} T ^{-1}\right]$
$(B)$ Co-efficient of Viscosity $(\eta)$
$(II)$ $\left[ M L ^2 T ^{-1}\right]$
$(C)$ Planck's Constant $(h)$
$(III)$ $\left[ M L ^{-1} T ^{-2}\right]$
$(D)$ Work Function $(\phi)$
$(IV)$ $\left[ M L ^2 T ^{-2}\right]$
Choose the correct answer from the options given below:
Match List $I$ with List $II$
| List $I$ | List $II$ |
| $(A)$ Young's Modulus $(Y)$ | $(I)$ $\left[ M L ^{-1} T ^{-1}\right]$ |
| $(B)$ Co-efficient of Viscosity $(\eta)$ | $(II)$ $\left[ M L ^2 T ^{-1}\right]$ |
| $(C)$ Planck's Constant $(h)$ | $(III)$ $\left[ M L ^{-1} T ^{-2}\right]$ |
| $(D)$ Work Function $(\phi)$ | $(IV)$ $\left[ M L ^2 T ^{-2}\right]$ |
Choose the correct answer from the options given below:
- [JEE MAIN 2023]
The force of interaction between two atoms is given by $F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is
The force of interaction between two atoms is given by $F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is
- [JEE MAIN 2019]
If force $(F)$, velocity $(V)$ and time $(T)$ are considered as fundamental physical quantity, then dimensional formula of density will be:
- [JEE MAIN 2023]
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express length in terms of dimensions of these quantities.
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express length in terms of dimensions of these quantities.
If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be fundamental quantities then energy has dimensional formula
If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be fundamental quantities then energy has dimensional formula