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

By putting the dimensions of each quantity on both the sides we get `[T^(-1)]=[M]^(x)[MT^(-2)]^(y)`
Now comparing the dimesions of quantities in both sides we get x+y=0 and 2y=1
`:. x=-(1)/(2),y=(1)/2`