The frequency of oscillation of a mass m suspended from a spring having force constant k is given by `f = Cm^(x)k^(g)`, where C is a dimensionless quantity. The value of x and y

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)`

Explanation

`f=C m^(x)k^(y)[k]=M^(1)L^(0)T^(-2)`
Comparing dimensional formula on both sides,
`M^(0)L^(0)T^(-1)=M^(x)(M^(1)L^(0)T^(-2))^(y)`
`=M^(x)xxM^(y)M^(y)L^(0)T^(-2y)`
`M^(0)L^(0)T^(-1)=M^(x+y)L^(0)T^(-2y)`
Comparing dimensional formula on both side
`0x+y and -1=-2y`
`:.y=(1)/(2)So, 0=x+(1)/(2)`
`:.x=-(1)/(2)`