Question

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

Answer 1

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+2bT−a+c]

Applying the principle of homogeneity of dimensions,

we get

a=1                ...(ii)

a+2b=2             ...(iii)

−a+c=−2             ...(iv)

On solving eqs. (ii), (iii) and (iv), we get

a=1,b=1/2,c=−1

[E]=[p1A1/2t−1]