If momentum (p), area (A) and time (t) are taken to be fundamental quantities, then energy has the dimensional formula

Question

Infinity Learn · Accepted Answer

Let energy E $$=$$ kpaAbtc…..(i)Where$$ k is a dimensionless constant of proportionality.Equating dimensions on both sides of $$(i), we get[$$ML2T-2$$]  $$=$$ [$$MLT-1$$]a[$$M0L2T0$$]b[$$M0L0T$$]c                    $$=$$ [ $$MaLa+2bTa+c$$]Applying the principle of homogeneity of dimensionswe geta $$=$$ $$1$$            …(ii)a+2b$$ $$=$$ $$2$$ …$$(iii)-a+c$$ $$=-2$$ …..$$(iv)On$$ solving eqs. $$(ii), (iii) and (iv) we geta $$=$$ $$1$$, b $$=$$ $$12$$, c $$=$$ $$-1$$∴$${E$$] $$=$$ [$$p1A12t-1$$]

If momentum (p), area (A) and time (t) are taken to be fundamental quantities, then energy has the dimensional formula

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material