$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C\, ln\, (BD)$ holds true. Then which of the combination is not a meaningful quantity ?
$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C\, ln\, (BD)$ holds true. Then which of the combination is not a meaningful quantity ?
- [JEE MAIN 2016]
- A
$\frac{C}{{BD}} - \frac{{A{D^2}}}{C}$
- B
${A^2} - {B^2}{C^2}$
- C
$\frac{A}{B} - C$
- D
$\frac{{\left( {A - C} \right)}}{D}$
Similar Questions
Match List$-I$ with List$-II.$
List$-I$
List$-II$
$(a)$ Torque
$(i)$ ${MLT}^{-1}$
$(b)$ Impulse
$(ii)$ ${MT}^{-2}$
$(c)$ Tension
$(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension
$(iv)$ ${MI} {T}^{-2}$
Choose the most appropriate answer from the option given below :
Match List$-I$ with List$-II.$
| List$-I$ | List$-II$ |
| $(a)$ Torque | $(i)$ ${MLT}^{-1}$ |
| $(b)$ Impulse | $(ii)$ ${MT}^{-2}$ |
| $(c)$ Tension | $(iii)$ ${ML}^{2} {T}^{-2}$ |
| $(d)$ Surface Tension | $(iv)$ ${MI} {T}^{-2}$ |
Choose the most appropriate answer from the option given below :
- [JEE MAIN 2021]
If $L$ and $R$ are respectively the inductance and resistance, then the dimensions of $\frac{L}{R}$ will be
If $L$ and $R$ are respectively the inductance and resistance, then the dimensions of $\frac{L}{R}$ will be
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
Which of the following quantities has the same dimensions as that of energy
Which of the following quantities has the same dimensions as that of energy
Let us consider an equation
$\frac{1}{2} m v^{2}=m g h$
where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.
Let us consider an equation
$\frac{1}{2} m v^{2}=m g h$
where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.