question_answer

Consider a mass M moving in the positive r- direction with an acceleration a as shown below. The minimum acceleration needed to hold a smaller mass m stationary with respect to M on the vertical side of M is (Assume that the surfaces of M and m in contact are rough)

A)  \[\frac{g}{m}\]                                                

B)  \[\frac{g}{M}\]

C)   \[3g\]                                 

D)  \[\frac{g}{\mu }\]

Correct Answer: D

Solution :

  Free body diagram of mass m \[{{f}_{s}}\ge (m+M)g\] \[\mu N\ge (m+M)g\] \[\mu (m+M)a\ge (m+M)g\] \[a\ge \frac{g}{\mu }\]