Sometimes it is convenient to construct a system of units so that all quantities can be expresse...

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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 \( ]=\left[x^{\alpha}\right] ;[ \) speed \( ]=\left[x^{\beta}\right] \); \( [ \) acceleration \( ] \) \( =\left[x^{p}\right] ;[ \) linear momentum \( ]=\left[x^{q}\right] ;[ \) force \( ]=\left[x^{r}\right] \). Then
(a) \( \alpha+p=2 \beta \)
(b) \( p+q-r=\beta \)
(c) \( p-q+r=\alpha \)
(d) \( p+q+r=\beta \)
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