Ex-4.10   
 Group velocity is found out from Eq. 4.18.

 Since k=2*pi/w ; Vphase= w/k 

 w/k = sqrt(g/k)
 
 w=sqrt(g*k)

differetiating on both sides

dw=1/2 * sqrt(g) * k^-1/2 * dk

 dw= 1/2 * sqrt(g/k)
 
Hence Vgroup= Vphase/2