initial Angular momentum=Iw

final angular momentum={I+mr^2}w1

w1=Iw/{I+mr^2}=0.0005(4.7)/{0.0005+0.0002}=5/7(4.7)=nearly 3.4 rad/s

u have to use the given value of MI of the record....how did u assume that it is a disc.?if u do, then u have to use the calculated value in both expressions for AM. uve used the given value of I in the initial case and calculated 0.5mr^2 for the second, so ur answer is bound to be wrong!!