The frequency of oscillation ( f ) of a liquid drop depends on its radius ( r ), density ( ), and the surface tension ( S ) of the liquid. If the percentage errors in the measurement of r , , and S are 2 % , 2 % , and 4 % respectively, then the maximum percentage error in the calculated value of the frequency f is :

Step-by-step solution

Let the relation be f = k r^a ^b S^c , where k is a dimensionless constant. Writing the dimensional formulas for each quantity: [f] = T ⁻¹ [r] = L [ ] = M L ⁻³ [S] = M T ⁻² Equating the dimensions on both sides: T ⁻¹ = ( L )^a ( M L ⁻³)^b ( M T ⁻²)^c T ⁻¹ = M ^ b+c L ^ a-3b T ^ -2c Comparing the exponents of M, L, and T: b + c = 0 a - 3b = 0 -2c = -1 c = 1 2 Substituting c into the first equation: b + 1 2 = 0 b = - 1 2 Substituting b into the second equation: a - 3 (- 1 2 ) = 0 a = - 3 2 The relation is f = k r^ -3