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 dimensionless 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]^(0)[MT^(-2)]^(0)`
Now comparing the dimension of quantities in both sides we get `x + y = 0 and 2y = 1:. X = (1)/(2), y = (1)/(2)`