A) \[1.764N\]
B) \[0.1764N\]
C) \[0.3N\]
D) it will not slide for any F
Correct Answer: A
Solution :
In the given situation there are two possibilities if the force applied on body \[A\] is less than a certain value, both of them move together as a combined system with same acceleration and if the force applied on body \[A\] is greater than a certain value, both the bodies will move with different accelerations. First possibility: If both are moving with a common acceleration, the common acceleration of the system will be,\[a=\frac{F}{m+M}\]where \[m\] is the mass of body \[B\] and \[M\] is the mass of body\[A\]. So, the contact force acting on the body \[B\] to provide acceleration a in it must be \[F=ma=m-\frac{F}{m+M}\] Now, as this force to the upper body \[B\] is provided by the friction between body \[A\] and body\[B\], both will move together only and only if this force is less than the force of limiting friction between \[A\] and\[B\]. In other words, the body \[B\] will begin to slide on body \[A\] if the contact force, \[m\frac{F}{m+M}\]greater than the force of limiting friction between body \[A\] and\[B\]. Thus, in the limiting condition, for body \[B\] to just begin to slide on body\[A\], \[m\frac{F}{m+M}=\mu mg\] or \[F=\mu (m+M)g\] \[=0.15(0.2+1)9.8\] \[=1.764\,\,N\]
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