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=Cm^(x) K^y`
`implies ` { `Krarr` spring constant}
`{K=F/x=[MT^(-2)]}`
`implies[T^(-1)]=[M]^(x) [MT^(-2)]^y`
`implies[T^(-1)]=[M^(x+y)T^(-2y)]`
`2y=+1, y =1/2`
`implies x+y=0 , x =-1/2`