Explanation

Let radius of gyration $\lbrack k\rbrack \propto \lbrack h\rbrack^{x}\lbrack c\rbrack^{y}\lbrack G\rbrack^{z}$ By substituting the dimension of $\lbrack k\rbrack = \lbrack L\rbrack$ $\lbrack h\rbrack = \left\lbrack ML^{2}T^{- 1} \right\rbrack$ $\lbrack c\rbrack = \lbrack LT^{- 1}\rbrack$ $\lbrack G\rbrack = \lbrack M^{- 1}L^{3}T^{- 2}\rbrack$ And by comparing the power of both sides We can get $x = 1/2,\ y = - 3/2,\ z = 1/2$ Therefore dimension of radius of gyration is $\lbrack h\rbrack^{1/2}\lbrack c\rbrack^{- 3/2}\lbrack G\rbrack^{1/2}$