The frequency of vibration f of a mass m suspended from a spring of spring const

Question

The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f =C

m^{x} K^{y}

; where C is a dimensionless quantity. The value of x and y are

Options:

A . x = 12, y = 12

B . x = -12, y = - 12

C . x = 12, y = - 12

D . x = - 12, y = 12

Answer: Option D
:
D
By putting the dimensions of each quantity both sides we get

[T^{- 1}] = [M]^{x} [M T^{- 2}]^{y}

Now comparing the dimenstions of quantities in both sides we get x+y =0 and 2y =1

∴

x = -

\frac{1}{2}

,y =

\frac{1}{2}

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