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