The dimensions of length are expressed as `G^(x)c^(y)h^(z)`, where G, c and h are the universal gravitational constant, speed of light and Planck's constant respectively, then :

Options

A. x=(1/2), y=(1/2)
B. x = (1/2), z=(1/2)
C. y=(-3/2), z =(1/2)
D. y=(1/2), z = (3/2)

Answer

B, C

Explanation

Let `L=G^(x)c^(y)h^(z)`
`:.[M^(0)L^(1)T^(0)]=[M^(-1)L^(-3)T^(-2)]^(x)[LT^(-1)]^(y)[ML^(2)T^(-1)]^(z)`
or `[M^(0)L^(-1)T^(0)]=M^(-x+z)L^(3x+y+2z)T^(-2x-y-z)`
`:.-x+z=0,3x+y+2x=1,-2x-y-z=0`,
`:.x=(1)/(2),y=(-3)/(2),z=(1)/(2)`