A rolled yellow paper cylinder is rotating clockwise direction at a constant rate of 1 revolution / 60 seconds. A pencil is touching the paper cylinder and is moving from T1 to T2 in 10 seconds and stops for 10 seconds. Then it moves to T3 in next 40 seconds (total time=60 seconds) as shown in figure 2. What would be the graph on paper when it is unrolled?
The problem involves understanding the path of a pencil moving on a rotating cylindrical surface, which is then unrolled to form a flat paper. Here are the steps to determine the correct graph representation:
The paper cylinder makes 1 revolution every 60 seconds. In our problem, the timeline is divided into three stages:
From T1 to T2, the pencil moves for 10 seconds.
The pencil then stops moving for the next 10 seconds.
Finally, it moves to T3 over 40 seconds.
In the first 10 seconds, since the pencil is moving and the cylinder is rotating, the path on the unrolled paper is a diagonal line.
For the next 10 seconds, the cylinder continues to rotate while the pencil remains stationary, resulting in a horizontal line on the unrolled paper.
During the final 40 seconds, the pencil moves as the cylinder rotates, again creating a diagonal path.
Considering these steps, the unrolled rectangular paper will depict the pencil path as two diagonal segments separated by a horizontal segment. Thus, the correct representation of the graph on unrolled paper is:
