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