Q. A block B is placed on block A. The mass of block $B$ is less that 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
Explanation
(d) 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 $B$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.