A block B is placed on block A. The mass of b | vedclass

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(D) If the applied force $F$ is less than the limiting friction $f_l$ between block $A$ and $B$,both blocks move together with a common acceleration.$

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(D) If the applied force $F$ is less than the limiting friction $f_l$ between block $A$ and $B$,both blocks move together with a common acceleration.$a_A = a_B = \frac{F}{m_A + m_B}$Since $F$ increases linearly with time,the common acceleration also increases linearly with time.When the applied force $F$ exceeds the limiting friction $f_l$,the blocks begin to slip relative to each other.For block $B$,the net force is $F - f_k$,where $f_k$ is the kinetic friction. Thus,the acceleration of $B$ is $a_B = \frac{F - f_k}{m_B}$. Since $F$ continues to increase,$a_B$ increases with a steeper slope than before.For block $A$,the only horizontal force acting on it is the kinetic friction $f_k$ exerted by block $B$. Thus,the acceleration of $A$ is $a_A = \frac{f_k}{m_A}$. Since $f_k$ is constant,$a_A$ becomes constant after slipping begins.Comparing the slopes and behavior,graph $D$ correctly represents this: both accelerations increase together until slipping occurs,after which $a_B$ continues to increase while $a_A$ remains constant.

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