If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
- A
${h^{1/2}}{c^{ - 3/2}}{G^{1/2}}$
- B
${h^{1/2}}{c^{3/2}}{G^{1/2}}$
- C
${h^{1/2}}{c^{ - 3/2}}{G^{ - 1/2}}$
- D
${h^{ - 1/2}}{c^{ - 3/2}}{G^{1/2}}$
Similar Questions
If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is
If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is
Dimensional formula for angular momentum is
Dimensional formula for angular momentum is
- [AIPMT 1988]
The dimensional formula for Boltzmann's constant is
The dimensional formula for Boltzmann's constant is
- [AIIMS 2019]
Match List$-I$ with List$-II$
List$-I$
List$-II$
$(a)$ $h$ (Planck's constant)
$(i)$ $\left[ M L T ^{-1}\right]$
$(b)$ $E$ (kinetic energy)
$(ii)$ $\left[ M L ^{2} T ^{-1}\right]$
$(c)$ $V$ (electric potential)
$(iii)$ $\left[ M L ^{2} T ^{-2}\right]$
$(d)$ $P$ (linear momentum)
$( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]$
Choose the correct answer from the options given below
Match List$-I$ with List$-II$
| List$-I$ | List$-II$ |
| $(a)$ $h$ (Planck's constant) | $(i)$ $\left[ M L T ^{-1}\right]$ |
| $(b)$ $E$ (kinetic energy) | $(ii)$ $\left[ M L ^{2} T ^{-1}\right]$ |
| $(c)$ $V$ (electric potential) | $(iii)$ $\left[ M L ^{2} T ^{-2}\right]$ |
| $(d)$ $P$ (linear momentum) | $( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]$ |
Choose the correct answer from the options given below
- [JEE MAIN 2021]
A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let $R$ be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency $v$ about its equilibrium shape. By dimensional analysis, the ratio $\frac{v}{\sqrt{\sigma / \rho R^3}}$ can be (Here, $\sigma$ is surface tension, $\rho$ is density, $g$ is acceleration due to gravity and $k$ is an arbitrary dimensionless constant)
A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let $R$ be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency $v$ about its equilibrium shape. By dimensional analysis, the ratio $\frac{v}{\sqrt{\sigma / \rho R^3}}$ can be (Here, $\sigma$ is surface tension, $\rho$ is density, $g$ is acceleration due to gravity and $k$ is an arbitrary dimensionless constant)
- [KVPY 2012]