1.

The frequency of vibrations of a mass m suspended from a spring of spring const. k is given by v=cm^(x)k^(y), where c is a dimensionless constant. The values of x and y are respectively :

Answer»

`(1)/(2),(1)/(2)`
`-(1)/(2),-(1)/(2)`
`(1)/(2),-(1)/(2)`
`-(1)/(2),(1)/(2)`

Solution :`v=Cm^(x)k^(y).`
WRITING DIMENSIONS on both sides,
`[M^(0)L^(0)T^(-1)]=M^(x)[ML^(0)T^(-2)]^(y)`
`[M^(0)L^(0)T^(-1)]=[M^(x+y)T^(-2y)]`
Comparing dimensions on both sides, we have
`0=x+y`
and `-1=-2yimpliesy=(1)/(2)`
`:.x+(1)/(2)=0impliesx=-(1)/(2)`
So carrect choice is `(d)`.
Aliter. Remembering that FREQUENCY of oscillation of loaded spring is `v=(1)/(2PI)SQRT((k)/(m))=(1)/(2pi)(k)^(1//2).m^(-1//2)`
which gives `x=-(1)/(2)andy=(1)/(2)`


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