The frequency of vibration v of mass m suspended from a spring of spring constant k is given by `f=cm^(x)k^(y)` where c is a dimensional constant. The volumes of x and y are :

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

C

Explanation

`f=c.m^(x)k^(y)`
`[M^(0)L^(0)T^(-1)]=[M]^(x)[ML^(-2)]^(y)`
`[M^(x+y)T^(-2y)]`
`therefore x+y=0`
`x=-y`
`-2y=-1`
`therefore y=(1)/(2)`
`therefore x=-(1)/(2)`