Question

Find the acceleration of the block of mass M in the situation of figure. The coefficient of friction between the two blocks is µ1 and that between the bigger block and the ground is µ2.

Answer 1

Hey. Refers to the attachment for the answer.  "{Two Attachments}

The answer of this question was too difficult to find. It has a lot of confusion and involves some Tuf mathematical expressions which were causing problems to type on computer. Therefore, I have attached an attachment.

In the Attachment, I have solved whole question with a full details.

The Final answer is,

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" a =  [2m-µ2(M+m)]g/[M+m{5+2(µ1 -µ2)}]   "

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It has been derived there by using some concepts.  The Free body diagram of both the masses are drawn clearly.

To avoid the confusion in masses, I have taken M as K and mass m was as it is. In last I interchanged that. Thus got the answer.

Hope it helps.