x in the above equation h = h cot cot ° ° h cot ° = h cot ° + h(cot ° – cot ° ) = h = cot ° – cot ° = . m - - - - Appendix According to the principle of homogeneity, Dimensions of LHS = Dimensions of RHS Substituting the dimensions in the given formula S = ut + / at , is a number. It has no dimensions [L] = [LT - ] [T ]+[LT - ] [T ] [L] = [L] + [L] As the dimensional formula of LHS is same as that of RHS, the equation is dimensionally correct. Comment: But actually it is a wrong equation.
We know that the equation of motion is s = ut + / at So, dimensionally correct equation need not be the true (or) actual equation But a true equation is always dimensionally correct. . Round - off the following numbers as indicated. a) .
to digits b) . × to digits c) . × - to digits d) 124783 to digits. Solution: a) .
b) . × c) . × - d) 124780 . Solve the following with regard to significant figures.
a) b) . × . Convert a velocity of kmh - into m s - with the help of dimensional analysis. Solution: n = kmh - n = ?
m s - L = 1Km L =1m T = 1h T = 1s n = n L L T T b The dimensional formula for velocity is [L T - ] a = b = - n Km h s n s s = × × / =