The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants $G, h$ and $c$ . Which of the following correctly gives the Planck length?
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants $G, h$ and $c$ . Which of the following correctly gives the Planck length?
- [JEE MAIN 2018]
- A
$G^2hc$
- B
${\left( {\frac{{Gh}}{{{c^3}}}} \right)^{\frac{1}{2}}}$
- C
${G^{\frac{1}{2}}}{h^2}c$
- D
$Gh^2c^3$
Similar Questions
Match List $I$ with List $II$ :
List $I$ (Physical Quantity)
List $II$ (Dimensional Formula)
$(A)$ Pressure gradient
$(I)$ $\left[ M ^0 L ^2 T ^{-2}\right]$
$(B)$ Energy density
$(II)$ $\left[ M ^1 L ^{-1} T ^{-2}\right]$
$(C)$ Electric Field
$(III)$ $\left[ M ^1 L ^{-2} T ^{-2}\right]$
$(D)$ Latent heat
$(IV)$ $\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$
Choose the correct answer from the options given below:
Match List $I$ with List $II$ :
| List $I$ (Physical Quantity) | List $II$ (Dimensional Formula) |
| $(A)$ Pressure gradient | $(I)$ $\left[ M ^0 L ^2 T ^{-2}\right]$ |
| $(B)$ Energy density | $(II)$ $\left[ M ^1 L ^{-1} T ^{-2}\right]$ |
| $(C)$ Electric Field | $(III)$ $\left[ M ^1 L ^{-2} T ^{-2}\right]$ |
| $(D)$ Latent heat | $(IV)$ $\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$ |
Choose the correct answer from the options given below:
- [JEE MAIN 2023]
The force $F$ on a sphere of radius $'a'$ moving in a medium with velocity $'v'$ is given by $F = 6\pi \eta av$. The dimensions of $\eta $ are
The force $F$ on a sphere of radius $'a'$ moving in a medium with velocity $'v'$ is given by $F = 6\pi \eta av$. The dimensions of $\eta $ are
The dimensions of impulse are equal to that of
The dimensions of impulse are equal to that of
- [AIPMT 1996]
The dimension of stopping potential $\mathrm{V}_{0}$ in photoelectric effect in units of Planck's constant $h$, speed of light $c$ and Gravitational constant $G$ and ampere $A$ is
The dimension of stopping potential $\mathrm{V}_{0}$ in photoelectric effect in units of Planck's constant $h$, speed of light $c$ and Gravitational constant $G$ and ampere $A$ is
- [JEE MAIN 2020]
Applying the principle of homogeneity of dimensions, determine which one is correct. where $\mathrm{T}$ is time period, $\mathrm{G}$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.
Applying the principle of homogeneity of dimensions, determine which one is correct. where $\mathrm{T}$ is time period, $\mathrm{G}$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.
- [JEE MAIN 2024]