question_answer

            A rough vertical board has an acceleration \[a\] along the horizontal, so that a block of mass M pressing against it does not fall. The coefficient of friction between block and the board is:       

A) \[>\frac{a}{g}\]                

B)        \[<\frac{g}{a}\]

C) \[=\frac{a}{g}\]                

D)        \[>\frac{g}{a}\]

Correct Answer: D

Solution :

Key Idea: Frictional force between block and board should be dominant, so that the block does not fall. The free body diagram is as follows Force of friction \[=\mu R\] where,\[\mu \]is coefficient of friction and R is normal  reaction.               Also,         \[R=Ma\] Since, mass does not fall, frictional force is dominant. i.e.,        \[Mg<F\] \[\Rightarrow \]               \[Mg<\mu \,Ma\] \[\Rightarrow \]               \[\mu >\frac{g}{a}\]