NAEST 2020 The forces on the half smiley ball and the coaste

Question: As seen in the video, a half smiley ball is held against a coaster and then taken towards the left with a jerk. The horizontal force by the thumb on the coaster before the jerk is denoted by $T_B$ and that during the jerk by $T_D$. The horizontal force by the fingers before the jerk is denoted by $F_B$ and that during the jerk by $F_D$. Choose the correct option.

1. $T_B = F_B$
2. $T_D = F_D$
3. $T_D > F_D$ in some part of the jerk
4. $T_D < F_D$ in some part of the jerk

Solution: Options (A), (C) and (D) are correct.

Consider the ball and the coaster together as a system. Initially, the system is at rest. Its acceleration is zero. Hence, the net force on the system in the horizontal direction is zero. Thus, $T_B=F_B$.

As the system starts moving, it accelerates in the direction of force applied by the fingers. Thus, $F_D > T_D $ in the accelerating phase.

In the final phase, the system decelerates. Its acceleration is in the direction of force applied by the thumb. Thus, $T_D > F_D$ in decelerating phase.

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