Sometimes it is convenient to construct a system of units so that all quantities can be expressed in
terms of only one physical quantity. In one such system, dimensions of different quantities are given
in terms of a quantity X as follows: $$[position] = [𝑋^{\alpha}]; [speed] = [𝑋^{\beta}]; [acceleration] =[𝑋^{p}]; [linear momentum] = [𝑋^{q}]; [force] = [𝑋^{r}]$$. Then

A

$$\alpha + p - 2\beta$$

B

$$p + q - r = \beta$$

C

$$p - q + r = \alpha$$

D

$$p + q + r = \beta$$