The velocity, acceleration and force in two systems of units are related as under: (i) v′$$=$$α$$2$$βv (ii) a′$$=($$αβ$$)a$$ (iii) F′$$=1$$αβFAll the primed symbols belong to one system and unprinted ones belong to the other system. α and β arc dimensionless constants. Which of the following $$is/are$$ correct?

Question

The velocity, acceleration and force in two systems of units are related as under: (i) v′$$=$$α$$2$$βv    (ii) a′$$=($$αβ$$)a$$   (iii) F′$$=1$$αβFAll the primed symbols belong to one system and unprinted ones belong to the other system. α and β arc dimensionless constants. Which of the following $$is/are$$ correct?

Infinity Learn · Accepted Answer

Velocity $$=$$ $$length/time$$, acceleration $$=$$ $$length/(time)2$$⇒  Length $$=($$ velocity $$)2$$ acceleration   i.e.,  L′$$=v$$′$$2a$$′,$$L=v2a$$⇒ L′$$L=v$$′$$v2aa$$′$$=$$α$$2$$β$$21$$αβ$$=$$α$$3/$$β$$3Now$$, m′$$=F$$′a′,$$m=Fam$$′$$m=F$$′Faa′$$=1$$αβ×$$1$$αβ$$=1$$α$$2$$β$$2Time$$ $$=$$ velocity $$/$$ acceleration, i.e.,T′$$=v$$′a′ and $$T=vaT$$′$$T=v$$′vaa′$$=$$α$$2$$β$$1$$αβ$$=$$αβ$$2Momentum$$ $$=$$ mass x velocityp′$$=m$$′v′,$$P=mv$$,p′$$p=m$$′mv′$$v=1$$α$$2$$β$$2$$α$$2$$βα$$2$$β$$=1$$β$$3$$

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