In part (a) we have calculated work done from the ground frame of reference. Now, let us take plank as the reference frame.
Acceleration of plank
a0=fM=μmgM
Free body diagram of disc with respect to plank is shown in figure. Here, ma0 = pseudo force.
∴ Retardation of disc w.r.t. plank.
ar=f+ma0m=μmg+μm2gMmμg+μmgM
=(M+mM)μg
The disc will stop after travelling a distance Sr relative to plank, where
Sr=v2r2ar (0=v2r−2αrSr)
=Mgh(M+m)μg
∴ Work done by friction in this frame of reference
Wfr=−fSr=(μgh)[Mgh(M+m)μg]
=−Mmgh(M+m) which is same as part (a)
Note: Work done by friction in this problem does not depend upon the frame of reference, otherwise in general work depends upon reference frame.