Question Detail
Question
Write the dimensions of a/b in the relation P = (a - x²)/(bt), where P is the pressure, x is the distance, and t is the time.
Correct Answer
Option B is the correct answer.
Detailed Explanation
P has dimensions [ML⁻¹T⁻²]. x² has [L²], so a must have [L²] to subtract. Then (a - x²) has [L²]. bt must have dimensions such that (a - x²)/(bt) has [ML⁻¹T⁻²]. So [b][t] = [L²]/[ML⁻¹T⁻²] = [L²] × [M⁻¹L T²] = [M⁻¹L³T²]. Since t has [T], [b] = [M⁻¹L³T]. Then a/b = [L²] / [M⁻¹L³T] = [M L⁻¹ T⁻¹]. Not in options. Option B is ML⁰T⁰, which is mass. Not matching.
Hint
Use dimensional analysis.