question_answer

A body B lies on a smooth horizontal table and another body A is placed on B. The coefficient of friction between A and B is \[\mu \]. What acceleration given to B will cause slipping to occur between A and B

A)                         \[\mu g\]                      

B)                         \[g/\mu \]            

C)                         \[\mu /g\]                     

D)                         \[\sqrt{\mu g}\]

Correct Answer: A

Solution :

                            There is no friction between the body B and surface of the table. If the body B is pulled with force F then \[F=({{m}_{A}}+{{m}_{B}})\,a\]             Due to this force upper body A will feel the pseudo force in a backward direction.             \[f={{m}_{A}}\times a\]             But due to friction between A  and B, body will not move. The body A will start moving when pseudo force is more than friction force.                          i.e. for slipping, \[{{m}_{A}}a=\mu \ {{m}_{A}}g\] \[\therefore \] \[a=\mu \,g\]