Question

The velocity of an object varies with time as V=At cube+ Bt square+Ct+D .Find the dimensional formula for AB/CD?

Answer 1

Answer:

Dimensional formula of AB/CD = T⁻⁴

Explanation:

V = At³ + Bt² + Ct + D

Since we can add V, At³, Bt², Ct and D

dimensional formula of all these terms are the same that is,

Dimension of V = Dimension of At³ = Dimension of Bt² = Dimension of Ct = Dimension of D

[V] = [At³] = [Bt²] = [Ct] = [D]

We know that,

[V] = L T⁻¹

Hence equating we get,

[V] = [At³]

L T⁻¹ = [A] T³

[A] = L T⁻¹ * T⁻³

[A] = L T⁻⁴

[V] = [Bt²]

L T⁻¹ = [B] T²

[B] = L T⁻¹ * T⁻²

[B] = L T⁻³

[V] = [Ct]

L T⁻¹ = [C] T

[C] = L T⁻¹ * T⁻¹

[C] = L T⁻²

[V] = [D]

[D] = L T⁻¹

Therefore,

AB/CD = (LT⁻⁴)(LT⁻³)/(LT⁻²)(LT⁻¹)

AB/CD = (L² T⁻⁷) / (L² T⁻³)

AB/CD = L²⁻²  T⁻⁷⁺³

AB/CD = T⁻⁴