Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant $h$ and the speed of light $c$, as $Y=c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?
Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant $h$ and the speed of light $c$, as $Y=c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?
- [IIT 2023]
- A
$\alpha=7, \beta=-1, \gamma=-2$
- B
$\alpha=-7, \beta=-1, \gamma=-2$
- C
$\alpha=7, \beta=-1, \gamma=2$
- D
$\alpha=-7, \beta=1, \gamma=-2$
Similar Questions
The position of a particle at time $t$ is given by the relation $x(t) = \left( {\frac{{{v_0}}}{\alpha }} \right)\,\,(1 - {e^{ - \alpha t}})$, where ${v_0}$ is a constant and $\alpha > 0$. The dimensions of ${v_0}$ and $\alpha $ are respectively
The position of a particle at time $t$ is given by the relation $x(t) = \left( {\frac{{{v_0}}}{\alpha }} \right)\,\,(1 - {e^{ - \alpha t}})$, where ${v_0}$ is a constant and $\alpha > 0$. The dimensions of ${v_0}$ and $\alpha $ are respectively
A famous relation in physics relates 'moving mass' $m$ to the 'rest mass' $m_{0}$ of a particle in terms of its speed $v$ and the speed of light, $c .$ (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant $c$. He writes:
$m=\frac{m_{0}}{\left(1-v^{2}\right)^{1 / 2}}$
Guess where to put the missing $c$
A famous relation in physics relates 'moving mass' $m$ to the 'rest mass' $m_{0}$ of a particle in terms of its speed $v$ and the speed of light, $c .$ (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant $c$. He writes:
$m=\frac{m_{0}}{\left(1-v^{2}\right)^{1 / 2}}$
Guess where to put the missing $c$
Choose the correct match
List I
List II
$(i)$ Curie
$(A)$ $ML{T^{ - 2}}$
$(ii)$ Light year
$(B)$ $M$
$(iii)$ Dielectric strength
$(C)$ Dimensionless
$(iv)$ Atomic weight
$(D)$ $T$
$(v)$ Decibel
$(E)$ $M{L^2}{T^{ - 2}}$
$(F)$ $M{T^{ - 3}}$
$(G)$ ${T^{ - 1}}$
$(H)$ $L$
$(I)$ $ML{T^{ - 3}}{I^{ - 1}}$
$(J)$ $L{T^{ - 1}}$
Choose the correct match
|
List I |
List II |
|---|---|
|
$(i)$ Curie |
$(A)$ $ML{T^{ - 2}}$ |
|
$(ii)$ Light year |
$(B)$ $M$ |
|
$(iii)$ Dielectric strength |
$(C)$ Dimensionless |
|
$(iv)$ Atomic weight |
$(D)$ $T$ |
|
$(v)$ Decibel |
$(E)$ $M{L^2}{T^{ - 2}}$ |
|
$(F)$ $M{T^{ - 3}}$ |
|
|
$(G)$ ${T^{ - 1}}$ |
|
|
$(H)$ $L$ |
|
|
$(I)$ $ML{T^{ - 3}}{I^{ - 1}}$ |
|
|
$(J)$ $L{T^{ - 1}}$ |
- [IIT 1992]
From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is
From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is
- [JEE MAIN 2014]
Dimensional formula for torque is
Dimensional formula for torque is
- [AIIMS 2011]