Answer to Question #346281 in Quantum Mechanics for Fafa

Question

Use dimensional analysis to show the correct dimensions

for quantities below.

(8)

QUANTITY. DIMENSION

FORCE

POWER

PRESSURE

WORK, ENERGY

b. Prove that the equation F=ma is dimensionally correct

Answer 1

$[F]=[ma]=[M*LT^{-2}]$

$[P]=[Fv]=[MLT^{-2}*LT^{-1}]=[ML^2T^{-3}]$

$[p]=[F/A]=[MLT^{-2}/L^{2}]=[ML^{-1}T^{-2}]$

$[E]=[Fd]=[MLT^{-2}*L]=[ML^2T^{-2}]$