JEE: how do I do dimensional analysis to check if an equation is correct?

Dimensional analysis checks whether both sides of an equation have the same fundamental dimensions, written in terms of mass M, length L, and time T. The principle of homogeneity says every term that is added or equated must have identical dimensions. To use it, write each quantity in base dimensions: velocity is L T⁻¹, acceleration is L T⁻², force is M L T⁻², energy is M L² T⁻². Then substitute into the formula and compare both sides. For example, check v² = u² + 2as: v² is (L T⁻¹)² = L² T⁻², and 2as is (L T⁻²)(L) = L² T⁻², so both sides match and the formula is dimensionally consistent. If the dimensions do not match, the equation is definitely wrong. Remember it cannot catch missing dimensionless constants like 2 or ½, but it quickly flags major errors.