Question

Show that dimensionally the quantities Vq and (½)mv2
are equivalent. The
symbols carry the usual meaning

Answer 1

we have to show that,

quantities Vq and 1/2 mv² is dimensionally equivalent.

here, V is potential , q is charge , m is mass and v is speed

dimension of potential, V = [ML²T-³A-¹]

dimension of charge, q = [AT]

dimension of mass, m = [M]

dimension of speed, v = [LT-¹]

now, dimension of Vq = [ML²T-³A-¹][AT]

= [ML²T-²]

dimension of 1/2 mv² = [M][LT-¹]²

= [ML²T-²]

hence, it is clear that quantities Vq and 1/2mv² are dimensionally equivalent.