Question

Hello everyone. This is a question about Dimensional Analysis and I came across this question but I am unable to wrap my head around it. Its a new topic for me and am a bit confused how it works. The question seems simple but cant seem to get to the correct answer. The question:

An equation has three variables A,B and C.
A = B^2 + 2B^4/C . If the dimension of A is [L]^2/[T]^2, what must be the dimensions of B and C?

Options:
1. [B] = [L]^2/[T]^2 and [C] = [L]/[T]
2. [B] = [L]/[T] and [C] = [L]/[T]
3. [B] = [L]/[T] and [C] = (1/2)[T]/[L]
4. [B] = [L]/[T] and [C] = [T]/[L]
5. [B] = [L]/[T] and [C] = (1/2)[L]/[T]

Would be really helpful if someone could explain it. Thank you

Answer 1

2. [B] = [L]/[T] and [C] = [L]/[T]

Step-by-step explanation:

I assume you mean this:

A = B² + 2B⁴/C²

Since you can't add numbers with different units (for example, you can't add seconds to meters), each term in the sum must have the same units as A.

B² = [L]²/[T]²

B = [L]/[T]

B⁴/C² = [L]²/[T]²

C²/B⁴ = [T]²/[L]²

C² = B⁴ [T]²/[L]²

C² = ([L]/[T])⁴ [T]²/[L]²

C² = [L]²/[T]²

C = [L]/[T]

Notice we ignore the 2 coefficient, which is unitless.