A force F = t is applied to a block A as shown in figure, where t is time in seconds. The force is applied at t = 0 seconds when the system was at rest. Which of the following graph correctly gives the frictional force between A and horizontal surface as a function of time t. [Assume that at t = 0, tension in the string connecting the two blocks is zero].

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answer is C.

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Detailed Solution

Let $m A a n d m B$ be the mass of blocks A and B respectively. As the force F increases
from 0 to $μ S m A g$ , the frictional force f on block A is such that f = F. When $F = μ_{s} m_{A} g$ the frictional force f attains maximum value $f = μ_{s} m_{A} g$ . As F is further increased to $μ s m A + m B g$ the block A does not move. In this duration frictional force on block A remains constant at $μ s m A g$