Question

The position of a particle along the y-axis is $y = P t^4 + Q$. For dimensional consistency, the dimension of $P$ in terms of length [L] and time [T] is

• A. $L T^{-1}$
• B. $L T^{-2}$
• C. $L T^{-3}$
• D. $L T^{-4}$

Hint:

Always equate dimensions of every term in an equation; they must match exactly.

Answer 1

The Correct Option is D

Step 1: Apply dimensional analysis.
Given: $y = P t^{4} + Q$. Since $y$ has dimension [L] and $Q$ is a length constant, $P t^{4}$ must also have dimension [L].
Step 2: Determine the dimension of $P$.
$[P][T^{4}] = [L]$. Therefore, $[P] = \dfrac{[L]}{[T^4]} = L T^{-4}$.
Step 3: Conclusion.
Hence, the dimension of $P$ is $L T^{-4}$.