A block $B$ is placed on block $A$. The mass of block $B$ is less than the mass of block $A$. Friction exists between the blocks, whereas the ground on which the block $A$ is placed is taken to be smooth. $A$ horizontal force $F$, increasing linearly with time begins to act on $B$. The acceleration ${a_A}$ and ${a_B}$ of blocks $A$ and $B$ respectively are plotted against $t$. The correctly plotted graph is
A block $B$ is placed on block $A$. The mass of block $B$ is less than the mass of block $A$. Friction exists between the blocks, whereas the ground on which the block $A$ is placed is taken to be smooth. $A$ horizontal force $F$, increasing linearly with time begins to act on $B$. The acceleration ${a_A}$ and ${a_B}$ of blocks $A$ and $B$ respectively are plotted against $t$. The correctly plotted graph is
A block $B$ is placed on block $A$. The mass of block $B$ is less than the mass of block $A$. Friction exists between the blocks, whereas the ground on which the block $A$ is placed is taken to be smooth. $A$ horizontal force $F$, increasing linearly with time begins to act on $B$. The acceleration ${a_A}$ and ${a_B}$ of blocks $A$ and $B$ respectively are plotted against $t$. The correctly plotted graph is
If the applied force is less than limiting friction between block $A$ and $B$, then whole system move with common acceleration
i.e. ${a_A} = {a_B} = \frac{F}{{{m_A} + {m_B}}}$
But the applied force increases with time, so when it becomes more than limiting friction between $A$ and $B$, block $B$ starts moving under the effect of net force $F -F_k$
Where ${F_k} = $ Kinetic friction between block $A$ and $B$
$\therefore $ Acceleration of block $B$, ${a_B} = \frac{{F - {F_k}}}{{{m_B}}}$
As $F$ is increasing with time so $a_B$ will increase with time
Kinetic friction is the cause of motion of block $A$
$\therefore $ Acceleration of block $A$, ${a_A} = \frac{{{F_k}}}{{{m_A}}}$
It is clear that ${a_B} > {a_A}$.
i.e. graph (d) correctly represents the variation in acceleration with time for block $A$ and $B$.