The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by relation of the type f=cmxky, where c is a dimensionless constant. The values of x and y are

The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by relation of the type $f = c m^{x} k^{y},$ where c is a dimensionless constant. The values of x and y are

A
1/2, 1/2
B
–1/2, –1/2
C
1/2, –1/2
D
–1/2, 1/2

Solution:

$[M^{0} L^{0} T^{- 1}] = [M^{x}] [M^{y} T^{- 2 y}] = [M^{x + y} T^{- 2 y}]$

Equating powers of M and T.

$x + y = 0, - 2 y = - 1$

or $y = \frac{1}{2}, x + \frac{1}{2} = 0$

or $x = - \frac{1}{2}$

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