Suppose the volume V of some object happens to depend on timet according to the

Question

Suppose the volume V of some object happens to depend on timet according to the equation
V(t) = At3 + B/t, where A and B are someconstants. Let L and T denote dimensions of length and time,respectively. What are the dimensions of constant A and B? Suppose the volume V of some object happens to depend on timet according to the equation
V(t) = At3 + B/t, where A and B are someconstants. Let L and T denote dimensions of length and time,respectively. What are the dimensions of constant A and B?

Explanation / Answer

We know , Dimension of volume is [L3] So dimension of At3 should also be [L3] Dimension of t is time So A[T3] = [L3]    => A = [L3T-3] Similarly dimension of B/t should also be [L3] So B / [T] = [L3] B = [L3T]

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