The frequency `f` of vibrations of a mass `m` suspended from a spring of spring constant `k` is given by `f = Cm^(x) k^(y)` , where `C` is a dimensionnless constant. The values of `x and y` are, respectively,

Options

A. `x =1/2 , y = 1/2`
B. `x = -1/2 , y = -1/2`
C. `x = -1/2 , y = 1/2`
D. `x = 1/2 , y = 1/2`

Answer

C

Explanation

`n prop cm^x k^y`
`[n] = [ cm^x k^y]`
`[T^(-1)] = [M^x (F/x)^y ]`
`[M^0 L^0 T^(-1)] = [M^x ((MLT^(-2))/(L))y]`
Equating power of M,L and T
`0 = x + y`
`-1 = -2 y " " y = 1/2 , " " x = -1/2`