An inclined plane make an angle 30 with horizon a solid sphere rading down this plane from rest without Slipping has. linear acc equal to

net force on center of mass = mgsin@

friction force = f (acting upwards)

for linear motion ,

     mgsin@ - f = ma ..............1

for angular motion

             fR = I(alfa)     ........2        (alfa is angular accleration)

from 1 & 2

 mgsin@ = ma + I(alfa)/R         ...............3

now, if it is given that the body is rolling without slipping then we apply a = (alfa)R

now eq 3 becomes

 mgsin@ = ma + 2ma/5                              (Isphere = 2mR²/5)

         a = 5gsin@/7

            =5g/14                                        (sin30 = 1/2)