Which of the following equations are dimensionally consistent?
Answer:
(a)
The distance travelled by an object is
x = vt
Dimension of x is [L], dimension of v is [L]/[T] and dimension of t is [T].
Substitute [L] for x, [L]/[T] for v, and [T] for t,
The dimensions on both the sides are the same.
Thus, the equation x = vt is dimensionally consistent.
(b)
The distance travelled by an object is
The dimensions on both the sides are the same.
( c)
Given equation is
Note that 2 is ignored in dimensional analysis because it has no dimensions.
The dimensions on both the sides are the same.
