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Question

can it be stated that the result obtained does not depend on the choice of the reference frame.
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Solution

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=v2r2αrSr)

=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.

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