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.,        \[Mg<F\] \[\Rightarrow \] \[Mg<\mu \,\,Ma\] \[\Rightarrow \] \[\mu >\frac{g}{a}\]