Which of the following equations are dimensionally consistent?
Answer:
(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.