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 \[{{f}_{s}}\ge (m+M)g\] \[\mu N\ge (m+M)g\] \[\mu (m+M)a\ge (m+M)g\] \[a\ge \frac{g}{\mu }\]