$A, B, C$ 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
$\frac{{\left( {A - C} \right)}}{D}$
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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 massive black hole of mass $m$ and radius $R$ is spinning with angular velocity $\omega$. The power $P$ radiated by it as gravitational waves is given by $P=G c^{-5} m^{x} R^{y} \omega^{z}$, where $c$ and $G$ are speed of light in free space and the universal gravitational constant, respectively. Then,
A massive black hole of mass $m$ and radius $R$ is spinning with angular velocity $\omega$. The power $P$ radiated by it as gravitational waves is given by $P=G c^{-5} m^{x} R^{y} \omega^{z}$, where $c$ and $G$ are speed of light in free space and the universal gravitational constant, respectively. Then,
- [KVPY 2017]