Question

Write the dimension a×b
in the relation E = (b - x 2 ) / at , where E is energy, x is distance and t is time. Please show the method to solve this question.

Answer 1

By principle of homogeneity we know that, only like physical quantities (sometimes having same dimensions) can be added or subtracted.

So,

[b] = [x²] = [L²]

{If it is 2x then , [b] = L}

Now,

[E] = [ML²T-²]

[a] = [L²]/[E]×[T] = [L²] /ML²T-²T = [M-¹T]

Now,

[a×b]=[L²×M-¹T] = [M-¹L²T]

Cheers!