The time period of a large fluid star may depends upon its mean radius `R,` its mean density `(p)` and the gravitation constant `G`. Using dimensional consideration the value of `T` is :

Options

A. `kpRG`
B. `kp^(1/2)G^(1/2)`
C. `kp^(1/2)G^(-1/2)R^(0)`
D. `kp^(1/2)G^(-1)R^(0)`

Answer

C

Explanation

Here `M^(0)L^(0)T^(1)=R^(x)p^(y)G^(z)`
`=[L^(1)]^(x)[ML^(-3)]^(y)[M^(-1)L^(3)T^(-2)]^(z)`
`M^(y-z)L^(x-3y+3z)T^(-2z)`
`:.y-z=0` Solving we get
`-2z=1x=0,y=-(1)/(2),z=-(1)/(2)`
`x-3y+3z=0`
Hence correct choice is `(c )`.