Question

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?

• A. The dimension of linear momentum is $L^{-1}$
• B. The dimension of energy is $L^{-2}$
• C. The dimension of force is $L^{-3}$
• D. The dimension of power is $L^{-5}$

Answer 1

Answer: (A), (B), (C)

Angular momentum $\ell=MVR$
$\Rightarrow \left[\ell\right]=\frac{ML^{2}}{T} \because M\rightarrow$ dimensionless
$\therefore T=L^{2}\,\ell$ also dimensionless
Now $p=mv=\frac{ML}{T} \,\because M\left(is\right)$ dimensionless
$\therefore \left[p\right]=L^{-1}$
$\left[Energy\right]=\frac{ML^{2}}{T^{2}T}=\frac{L^{2}}{L^{2}L^{2}}=L^{-2}$
$\left[Power\right]=\frac{ML^{2}}{T^{2}T}=\frac{L^{2}}{L^{2}L^{2}L^{2}}=L^{-4}$
$\left[Force\right]=\frac{ML}{T^{2}}=\frac{L}{L^{2}L^{2}}=L^{-3}$