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] =[Xp]; [linear momentum] = [Xq]; [force] = [Xr]. Then -

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α+p=2β

p+q−r=β

p−q+r=α

p+q+r=β

answer is A.

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Detailed Solution

Given L=xα ……(1)LT−1=xβ ……(2)LT−2=xp ……(3)MLT−1=xq ……(4)MLT−2=xr ……(5)(1)(2)⇒T=xα−βFrom (3)xαx2(α−β)=xp⇒α+p=2β From (4) M=xq−β From (5)⇒xq=xrxα−β ⇒α+r−q=β----(6)Replacing value 'α' in equation (6) from (A)2β−p+r−q=β⇒p+q−r=β (B)Replacing value of 'β' in equation (6) from (A)2α+2r−2q=α+pα=p+2q−2r

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