Question

Prove the following equation is dimensionally correct

f= 1/2l √F×l/m​

Answer 1

Answer:

(i) Conversion of one system of units into another.

(ii) Checking the accuracy of various formulae.

(iii) Derivation of formula

Illustration : Check the accuracy of the relation

where ν is the frequency, l is length , T is tension and m is mass per unit length of the string.

Solution : The given relation is

Writing the dimensions on either side, we get

LHS = ν = [T-1] = [M0L0T-1]

RHS = 1/2l√T/m = [T-1]

As LHS = RHS

Dimensionally the formula is correct