Physics Dimensions Challenge MDCAT, NMDCAT,CH # 1 Page 15,16 PHYSICS

Dimensional analysis is a useful method in physics that helps check whether an equation is physically correct and also helps derive formulas. Every physical quantity has dimensions based on fundamental quantities such as length (L), mass (M), and time (T). A correct physical equation must satisfy the principle of homogeneity, which states that the dimensions on both sides of an equation must be the same. For example, in the equation S= 2 1​ at 2 , the numerical factor 1/2 has no dimensions. Since acceleration has dimensions [LT −2 ] and t 2 has dimensions [T 2 ], their product gives [L], which matches the dimension of displacement S. Therefore, the equation is dimensionally correct. Dimensional analysis can also be used to derive formulas. For instance, centripetal force depends on mass, speed, and radius. By expressing these quantities in dimensional form and comparing powers of dimensions on both sides, a possible formula for centripetal force can be obtained. Thus, dimensional analysis is an important tool for verifying and developing physical relationships.