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 $\alpha_{4}$ and $\alpha_{\beta}$ of blocks A and B respectively are plotted against t. The correctly plotted graph is
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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
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
Acceleration of block A, $a_{A} = \frac{F_{k}}{m_{A}}$
It is clear that $a_{B} > a_{A}$ . i.e. graph correctly represents the variation in acceleration with time for block A and B.
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