If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G,\,c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then
If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G,\,c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then
- [IIT 1992]
- A
$x = \frac{1}{2},\,\,y = \frac{1}{2}$
- B
$x = \frac{1}{2},\,\,z = \frac{1}{2}$
- C
$y = - \frac{3}{2},\,\,z = \frac{1}{2}$
- D
$(b)$ and $(c)$ both
Similar Questions
Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then
Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then
- [IIT 1998]
If force $[F],$ acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities. Find the dimensions of energy.
If force $[F],$ acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities. Find the dimensions of energy.
- [NEET 2021]
$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be
$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be
- [JEE MAIN 2023]
If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is
If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is
- [JEE MAIN 2021]
Match List $I$ with List $II$
LIST$-I$
LIST$-II$
$(A)$ Torque
$(I)$ $ML ^{-2} T ^{-2}$
$(B)$ Stress
$(II)$ $ML ^2 T ^{-2}$
$(C)$ Pressure of gradient
$(III)$ $ML ^{-1} T ^{-1}$
$(D)$ Coefficient of viscosity
$(IV)$ $ML ^{-1} T ^{-2}$
Choose the correct answer from the options given below
Match List $I$ with List $II$
| LIST$-I$ | LIST$-II$ |
| $(A)$ Torque | $(I)$ $ML ^{-2} T ^{-2}$ |
| $(B)$ Stress | $(II)$ $ML ^2 T ^{-2}$ |
| $(C)$ Pressure of gradient | $(III)$ $ML ^{-1} T ^{-1}$ |
| $(D)$ Coefficient of viscosity | $(IV)$ $ML ^{-1} T ^{-2}$ |
Choose the correct answer from the options given below
- [JEE MAIN 2023]