Question

Let us consider a system of units in which mass and angular momentum are dimensionless. If the length has dimension of L, then the dimension of power is

Answer 1

Correct option is B. $$L^{-4}$$

$$[M] = mass = M^0L^0T^0$$

$$J(R)$$ = angular momentum

$$e = mvR = \dfrac{mL^2}{T}$$

$$m \rightarrow$$ Dimensionless

$$T = L^{2}$$

L is also Dimensionless

Now $$P = mv = \dfrac{mL}{T}$$

m is dimensionless

$$[P] = L^{-1}$$

Power = $$\dfrac{mL^2}{T^2 . T} = \dfrac{L^2}{L^2T^2L} = L^{-4}$$