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 both the sides we get `[T^-1]=[M]^x[MT^-2]^y`
now comparing the dimensions of quantities in both sides we get `x+y=0` and `2y=1` `because` `x=-(1)/(2)`,`y=(1)/(2)`