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

D

Explanation

`f=c m^(x)k^(y)`,
Spring constant `k="force/length."`
`[M^(0)L^(0)T^(-1)]=[M^(x)(MT^(-2))y]=[M^(x+y)T^(-2y)]`
`rArr" "x+y=0, -2y=-1 or y=(1)/(2) and x=-(1)/(2)`