Question

time period of oscillation of a streched string T depends on force constant k=F/L and mass m of string derive its expression using dimensional analysis​

Answer 1

Answer:

$T = \lambda \sqrt{ \frac{m}{k} }$

Explanation:

✓ We know that Dimensional Formula of F : Newton = kg.m/s^2 = [ MLT^(-2) ]

Hence,

$[ T] = [k] {}^{ \alpha } [m] {}^{ \beta } = [ MT {}^{ - 2} ] {}^{ \alpha } [ M] {}^{ \beta }$

✓ Form equations : α + β = 0 ; -2α = 1

=> α = -0.5 , β = 0.5

• Note that the dimensional analysis only provides the proportionality and therefore we need a proportionality constant λ