Question

The displacement x of a particle is given by x = a + bt + ct², where t is time in second and displacement x is in meter. Find the dimensions of a,b and c.

Answer 1

Dimensions of c = Dimensions of t = [M⁰L⁰T¹]

Dimensions of at² = Dimensions of v

∴ Dimensions of a = Dimensions of \(\frac{v}{t^2}\)

= \(\frac{L^1T^{-1}}{T^2}\) = L¹T^-3

= [M⁰L¹T^-3]

Similarly, dimensions of \(\frac{b}{(c+t)}\) = Dimensions of v

∴ Dimensions of b = Dimensions of v

= L¹T^-1 x T¹ = L¹

= [M⁰L¹T⁰]

Dimensions of a = [M⁰L¹T⁰]

Dimensions of b = [M⁰L¹T^-1]

Dimensions of c = [M⁰L¹T^-2]