Correct Option (d) x = -1/2, y = 1/2
Explanation:
f = amxky,
Dimensions of frequency f = [M0L0T-1]
Dimensions of constant a = [M0L0T0]
Dimensions of mass m = [M]
Dimensions of spring constant k = [MT-2]
Putting these value in equation (i), we get
[M0L0T-1] = [M]x [MT-2]y
Applying principle of homogeneity of dimensions, we get
x + y = 0 ...(i)
-2y = -1 ....(iii)
or y = 1/2, x = -1/2