CBSE Class 11 Physics Chapter 3: Motion in a Straight Line NCERT Solutions

An object can be considered approximately a point object if its size is very small compared to the distances it travels or the scale of the motion being observed. Let's analyze each case:

1. A railway carriage moving without jerks between two stations: The distance between two stations is typically very large compared to the size of a railway carriage. Therefore, the carriage can be reasonably approximated as a point object for this motion.
2. A monkey sitting on top of a man cycling smoothly on a circular track: The size of the monkey (and the man) is very small compared to the radius of the circular track. Thus, the monkey can be considered a point object in this context.
3. A spinning cricket ball that turns sharply on hitting the ground: The distance over which a cricket ball turns sharply after hitting the ground is often comparable to the size of the ball itself. Therefore, the ball cannot be treated as a point object in this scenario.
4. A tumbling beaker that has slipped off the edge of a table: The height of the table from which the beaker slips is usually not significantly larger than the dimensions of the beaker. Hence, the beaker cannot be accurately represented as a point object.

Based on this analysis, the correct options are (a) and (b).

Let's analyze the provided position-time (x-t) graphs to determine the correct statements:

1. (A) lives closer to the school than (B): The graph shows that child A's home (P) is at a smaller position value (closer to the origin O, the school) than child B's home (Q). Therefore, A lives closer to the school.

2. (A) starts from the school earlier than (B): The graph indicates that child A's journey starts at time $t\; =\; 0$ (the graph begins at the origin). Child B's journey starts at a later time, as their graph begins at a positive value of $t$ when $x\; =\; 0$. Thus, A starts earlier.

   For A: $x\; =\; 0$ at $t\; =\; 0$

   For B: $x\; =\; 0$ at $t\; >\; 0$

3. (A) walks faster than (B): The speed of an object is represented by the slope of its position-time graph. Observing the graph, the slope of B's line is steeper than the slope of A's line. A steeper slope means a higher speed. Therefore, B walks faster than A.

   Slope of B > Slope of A

   Speed of B > Speed of A

4. A and B reach home at the (same) time: The graph shows that both children's position-time graphs end at the same final time value, indicating they reach their respective homes simultaneously.

   Final time for A = Final time for B

5. (B) overtakes (A) on the road (once): An overtaking occurs when one object, initially behind, catches up to and passes another. In the x-t graph, this is represented by the intersection of their paths after starting. Since B starts later but moves faster, B will eventually catch up to A. The graph shows a single intersection point after both have started, indicating that B overtakes A once.

   Intersection point implies same position at the same time.