# Which of the following equations are dimensionally consistent?

Which of the following equations are dimensionally consistent?

(A) Consider the equation v = at
Carry out a dimension analysis on both sides.
The dimension of the left-hand side =

The dimensions on both sides are the same.
Thus, the equation v = at is dimensionally consistent.

(B) Consider the equation
Write the dimensions on both sides.
The dimension of the left-hand side =

The dimensions on both sides are different.
Thus, the equation is dimensionally inconsistent.

( C) Consider the equation
Carry out a dimension analysis on both sides.
The dimension of the left-hand side = [ T ]

The dimensions on both sides are different.
Thus, the equation is dimensionally inconsistent.

(D) Consider the equation
Carry out a dimension analysis on both sides.
The dimension of the left-hand side =
=

The dimension of the right-hand side

The dimensions on both sides are the same.
Thus, the equation is dimensionally consistent.

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