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28, , Units and Weasurement, , , , \ (T) and mass per unit length of the string (m)., Tet Vee To et, veke@ 7 mo ve U), Where a, b, ¢ are the dimensions and k is the dimensionless proportionality constant., , Writing the dimensions on both sides we get,, [M° 1? tener (mit?) [wo], [m° 1° T]=[ br patb-c Ta, , Comparing the dimensions on both sides we get,, , —2b=-] 2 ee, 2, 1 1, bac =0) SS = +c=0 a3 c=-—, 2 2, a+b-c=0 Ss a4 545-0 — ate li— 0) “ a=-l, , Substituting the values ofa, b andc in equation (1) we get,, , vek eo pl? _nl2, , k(T 1/2, 1G), , k 10, v=—,/—, £\m, 71. Mention any two limitations of dimensional analysis. (2 marks), , Ans: 1. It does not give any information whether a physical quantity is a scalar or a vector., 2. It gives no information about the dimensionless constants like 1, > wT etc, ina, , formula., , 3. This method cannot be used to study the relations involving trigonometric and, exponential functions., , 4. This method cannot be used to derive the formula of a physical quantity that depends, , on more parameters than the fundamental quantities,, , (Any Two), , ete