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] = [Xα] ; [speed] = [Xβ] ; [acceleration] = [Xρ] ; [linear momentum] = [Xq] ; [force] = [Xr] . Then [Adv. 2020]
a. α+p=2β
b. p+q−r=β
c. p−q+r=α
d. p+q+r=β