Question

The freuency of vibration f of a mass m suspended from a spring of spring constant k is given a relation f= am^xk^y where a is a dimentionalless constant . the values of x and y are...​

Answer 1

answer : x = -1/2 and y = -1/2

explanation : we know, dimension of frequency, f = [T-¹]

dimension of mass, m = [M]

from spring force , F = kx

dimension of spring constant, k = dimension of F/dimension of x

= [MLT-²]/[L] = [MT-²]

a/c to question, relation between f, m and k is given by, f = cm^xk^y where c is a dimensionless constant.

now putting their dimensions value in relation.

i.e., [T-¹] = c[M]^x [MT-²]^y

or, [T-¹] = c[M]^(x + y) [T]^(-2y)

on comparing both sides, we get

-1 = -2y => y = 1/2

x + y = 0 => x = -y = -1/2

hence, x = -1/2 And y = 1/2