# A quantity $f$ is given by $f=\sqrt{\frac{h c^{5}}{G}}$ where $\mathrm{c}$ is speed of light, $\mathrm{G}$ universal gravitational constant and $h$ is the Planck’s constant. Dimension of $f$ is that of:

Question:

A quantity $f$ is given by $f=\sqrt{\frac{h c^{5}}{G}}$ where $\mathrm{c}$ is speed of light, $\mathrm{G}$ universal gravitational constant and $h$ is the Planck’s constant. Dimension of $f$ is that of:

1. area

2. energy

3. momentum

4. volume

JEE Main Previous Year Single Correct Question of JEE Main from Chemistry Laws of Motion chapter.

JEE Main Previous Year 2019

Correct Option: 2

Solution:

Dimension of $[h]=\left[M L^{2} T^{-1}\right]$

\begin{aligned} &{[\mathrm{C}]=\left[L T^{-1}\right]} \\ &{[G]=\left[M^{-1} L^{3} T^{-2}\right]} \end{aligned}

Hence dimension of

\begin{aligned} &{\left[\sqrt{\frac{h C^{5}}{G}}\right]=\frac{\left[M L^{2} T^{-1}\right] \cdot\left[L^{5} T^{-5}\right]}{\left[M^{-1} L^{3} T^{-2}\right]}} \\ &=\left[M L^{2} T^{-2}\right]=\text { energy } \end{aligned}

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