The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation f=cmxky; where c is a dimensionless quantity. The value of x and y are

Asked by Anil | 19th May, 2017, 12:30: PM

Expert Answer:

Given relation
f = cmxky
where f = Frequency of vibration
       m = Mass suspended from a spring
        k = Spring constant
        c = Dimensionless quantity 
By putting the dimensions of each quantity on both the sides, we get
[T−1 ] = [M]x [MT−2 ] y
 
On comparing the dimensions of quantities on both sides, we get
x + y = 0 and 2y = 1
 
→ y = 1/2
 
and x = −1/2

Answered by Yashvanti Jain | 19th May, 2017, 05:13: PM