Static Friction

Static friction is a self-adjusting force that exactly balances the applied horizontal force as long as the body remains stationary, ranging from zero up to a maximum value of ${\mu }_{s}N$. While the push is small, friction grows to match it so the net force stays zero and the crate does not accelerate. Only when the applied force exceeds the limiting static friction does the crate begin to slide. The option claiming friction stays fixed at its maximum is wrong because static friction takes whatever value is needed below that ceiling. The kinetic-friction option is incorrect since kinetic friction only appears once relative sliding starts. The zero-friction option is wrong because a balancing force must exist to keep the net force zero against the push. This matches the NCERT description of the static friction regime preceding motion. As a plausibility check, everyday experience shows a gentle push moves nothing while a strong push suddenly starts the slide, exactly what a variable static friction predicts.