A person stands at the middle point of a wooden ladder which starts slipping between a vertical wall and the floor of a room, while continuing to remain in a vertical plane. The path traced by a person standing at the middle point of the slipping ladder i

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Q: 150 (IAS/2004)
A person stands at the middle point of a wooden ladder which starts slipping between a vertical wall and the floor of a room, while continuing to remain in a vertical plane. The path traced by a person standing at the middle point of the slipping ladder is:

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,4,11,4,4,4,3

keywords: 

{'wooden ladder': [0, 0, 1, 0], 'ladder': [0, 0, 1, 0], 'parabolic path': [0, 0, 2, 0], 'elliptical path': [0, 0, 1, 2], 'circular path': [0, 0, 1, 2], 'path': [1, 0, 4, 2], 'straight line': [1, 0, 3, 15], 'vertical plane': [0, 0, 2, 1], 'vertical wall': [0, 0, 2, 0], 'person': [3, 1, 18, 13], 'middle point': [0, 0, 1, 0], 'floor': [1, 1, 1, 5]}

The path traced by a person standing at the middle of a slipping ladder would indeed be a circular path. To understand why other options are incorrect, let`s examine each:

Option 1: A straight line implies that the person would move either vertically or horizontally, which won`t happen because the ladder`s top is slipping down the wall and the bottom is slipping out.

Option 2: An elliptical path implies that the person`s motion has two different principal radii - a major and a minor radius. However, the pivot point, at the point where the ladder touches the wall and the movement of the person, maintains a constant radius.

Option 4: A parabolic path is associated with freely falling objects under gravity or projectile motion. But, the person here is not under such conditions.

Hence, a circular path (Option 3) illustrates the person`s motion accurately. Here, the point of contact between the wall and ladder acts as the pivot, and the mid-point of the ladder traces a half-circle as the ladder falls.