CBSE Class 9 Science Chapter 8: Motion NCERT Solutions

Solution:

Yes, it is possible for an object to have zero displacement even if it has moved through a non-zero distance. Displacement is defined as the shortest distance between the initial and final positions of an object. If an object returns to its starting point, its displacement is zero, regardless of the path it took or the total distance covered.

Example: Consider an object moving along a circular path. If the object starts at a point A on the circle and completes one full revolution, it returns to 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, the displacement is zero.

Solution:

Given:

• Side of the square field = 10 m
• Time taken to complete one round = 40 s
• Total time elapsed = 2 minutes 20 seconds

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

Perimeter = 4 × side = 4 × 10 m = 40 m

This means the farmer covers a distance of 40 m in 40 s. Now, let's convert the total time elapsed into seconds:

Total time = 2 minutes + 20 seconds = (2 × 60) seconds + 20 seconds = 120 seconds + 20 seconds = 140 seconds

We can find the total distance covered by the farmer in 140 seconds. Since the farmer covers 40 m in 40 s, the speed of the farmer is:

Speed = Distance / Time = 40 m / 40 s = 1 m/s

The total distance covered in 140 seconds is:

Total distance = Speed × Total time = 1 m/s × 140 s = 140 m

To find the displacement, we need to determine the farmer's final position after covering 140 m along the boundary. The number of rounds completed by the farmer is:

Number of rounds = Total distance / Perimeter = 140 m / 40 m = 3.5 rounds

This means the farmer completes 3 full rounds and then half of another round. After 3 full rounds, the farmer is back at the starting point. In the next half round (0.5 round), the farmer moves along the boundary to the diagonally opposite corner of the square field. Let the initial position be A. After 3.5 rounds, the farmer will be at point C, which is diagonally opposite to A. The displacement is the magnitude of the straight line distance between the initial position (A) and the final position (C). Using the Pythagorean theorem for the diagonal of the square:

Displacement (AC) = \(\sqrt{\text{side}^2 + \text{side}^2}\) = \(\sqrt{10^2 + 10^2}\) = \(\sqrt{100 + 100}\) = \(\sqrt{200}\) = \(\sqrt{100 \times 2}\) = 10\(\sqrt{2}\) m

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

Solution:

Let's analyze the given statements:

1. It cannot be zero: This statement is false. Displacement can be zero if the object returns to its initial position, even if it has traveled a significant distance. For example, completing a full circle or a full round on a track results in zero displacement.
2. 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. The magnitude of displacement 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.

Since both statements (a) and (b) are false, neither is true for displacement.