CBSE Class 9 Science Chapter 8 Motion NCERT Solutions

Yes, it is possible for an object to have zero displacement even if it has moved through a certain distance. Displacement is defined as the shortest distance between the initial and final positions of an object. If the object's final position is the same as its initial position, then the displacement is zero.

Example: Consider an object moving along the circumference of a circle. If the object starts at a point A on the circle and completes one full revolution, it returns to the same point A. In this case, the distance traveled by the object is equal to the circumference of the circle, which is a non-zero value. However, since the object's final position is the same as its initial position, its displacement is zero.

Given:

Side of the square field = 10 m

Time taken for one round = 40 s

First, let's calculate the perimeter of the square field:

Perimeter = 4 × side

Perimeter = 4 × 10 m = 40 m

The farmer moves along the boundary, so in 40 seconds, the farmer covers a distance of 40 m.

Now, let's determine the total time in seconds:

Total time = 2 minutes 20 seconds

Total time = (2 × 60) seconds + 20 seconds

Total time = 120 seconds + 20 seconds = 140 seconds

Next, we calculate the total distance covered by the farmer in 140 seconds. Since the farmer covers 40 m in 40 s, the speed is 1 m/s.

Distance covered in 140 s = Speed × Time

Distance covered = 1 m/s × 140 s = 140 m

Now, we find out how many rounds the farmer completes in 140 seconds. Each round covers the perimeter of the field (40 m).

Number of rounds = Total distance covered / Perimeter

Number of rounds = 140 m / 40 m = 3.5 rounds

This means the farmer completes 3 full rounds and then half of the fourth round. If the farmer starts at a corner (let's say A), after 3.5 rounds, they will be at the diagonally opposite corner (let's say C).

The displacement is the shortest distance between the initial position (A) and the final position (C). In a square field with side 10 m, the diagonal AC can be calculated using the Pythagorean theorem:

Displacement² = side² + side²

Displacement² = (10 m)² + (10 m)²

Displacement² = 100 m² + 100 m²

Displacement² = 200 m²

Displacement = √(200 m²)

Displacement = √(100 × 2) m

Displacement = 10√2 m

The direction of displacement would be from the initial corner to the diagonally opposite corner (e.g., North-East if starting from South-West).

Therefore, the magnitude of the displacement of the farmer at the end of 2 minutes 20 seconds is  10\sqrt{2}  m.

Let's analyze the given statements about displacement:

Statement (a): It cannot be zero. This statement is false. Displacement can be zero if the object's final position is the same as its initial position. For example, if an object moves in a circular path and completes one full revolution, it returns to its starting point, and its displacement is zero, even though it has traveled a significant distance.

Statement (b): Its magnitude is greater than the distance travelled by the object. This statement is also false. The magnitude of displacement is always less than or equal to the distance traveled. It is equal to the distance traveled only when the object moves in a straight line without changing its direction. In all other cases (like moving along a curved path or changing direction), the displacement is shorter than the distance traveled.

Conclusion: Neither statement (a) nor statement (b) is true for displacement.