Question

(a)/(t^(2)) = Fv = (beta)/(x^(2)) Find dimension formula for [a] and [beta] (here t = "time" ,F = "force", v = "velocity" , x = "distance")

Answer 1

Given:

(a)/(t^(2)) =  Fv  = (beta)/(x^(2))

t = "time" ,F = "force", v = "velocity" , x = "distance"

To Find:

dimension formula for [a] and [beta]

Solution:

• F = mass x acceleration
• Dimension formula of mass = [M]
• Dimension Formula of acceleration = [L][$T^{-2}$]
• Dimension Formula of Force = [M][L][$T^{-2}$]

• Dimension Formula of time = [T]

• Dimension Formula of velocity = [L][$T^{-1}$]

• Dimension Formula of distance = [L]

Therefore

• Dimension Formula of a , [a] = [F]x[v]x[t²]
• [a] = [M][L][$T^{-2}$][L][$T^{-1}$][T²] = [M][L²][$T^{-1}$]

• Dimension formula of beta , [beta] = [F]x[V]x[x²]

• [beta] = [M][L][$T^{-2}$]  [L][$T^{-1}$] [L²]
• [beta] = [M][$L^{4}$][$T^{-3}$]