Physics

# Suppose an attractive nuclear force acts between two protons which may be written as $F=Ce^{-kr}/r^{2}$. (a) write down the dimensional formula and appropriate $SI$ units

##### SOLUTION

Given that

$F=\dfrac{C{{e}^{-kr}}}{{{r}^{2}}}$

$F{{r}^{2}}=C{{e}^{-kr}}$

$C=\dfrac{F{{r}^{2}}}{{{e}^{-kr}}}$

${{e}^{-kr}}$ is a dimensional quantity.

Dimension of $F=\left[ ML{{T}^{-2}} \right]$

Dimension of ${{r}^{2}}=\left[ {{L}^{2}} \right]$

So, the dimension of $C=\left[ M{{L}^{3}}{{T}^{-2}} \right]$

SI unit of $C=N{{m}^{2}}$

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Subjective Medium Published on 18th 08, 2020
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