Question

The Volume Of An Object As A Function Of The Time Is Calculated By V=At^3+B/T, Where T Is A Time Measured In Seconds And V Is In Cubic Meters. Determine The Dimension Of A Constant A And B.

Answer 1

Dear Student,

◆ Answer -

Dimensions of A = [L3.T-3]

Dimensions of B = [L3.T1].

◆ Explanation -

Given equation -

V = At^3 + B/t

According to dimensional analysis, dimensions of all terms in a equation must be same.

[V] = [A].[t^3]

[L3] = [A].[T3]

[A] = [L3.T-3]

Also,

[V] = [B]÷[t]

[L3] = [B]÷[T]

[B] = [L3.T1]

Therefore, dimensions of [A] = [L3.T-3] and [B] = [L3.T1].

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