Question

The strong nuclear force inside a nucleus is given by $F=\frac{Ce^{-kr}}{r^{2}}$, where $r$ is position. Dimensions of $C$ and $k$ are, respectively,

• A. $\left[M^{2}L^{3}T^{-2}\right]$, $\left[L\right]$
• B. $\left[ML^{3}T^{-2}\right], \left[L^{-1}\right]$
• C. $\left[MLT^{-2}\right]$, $\left[L^{-1}\right]$
• D. $\left[ML^3T^{-2}\right], \left[L^{0}\right]$

Answer 1

Answer: (B)

$\left[C\right]=\left[Fr^{2}\right]=\left[MLT^{-2}\right]\left[L^{2}\right]=\left[ML^{3}T^{-2}\right], \left[k\right]=\left[\frac{1}{r}\right]=\left[L^{-1}\right]$