need help with inclined plane problem

tricky_tick

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siddharth

Work is Force X Displacement. Now Work is minimum when the net force is minimum
By drawing the Free Body Diagram for the block, you would arrive at
[tex] 0=ma=F - mg \sin \alpha - \mu mg \cos \alpha [/tex]
Differentiating F with respect to alpha and equating to zero you would get the required result