UPSC Prelims 2004 · General Studies
Question 150: Basic Numeracy
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 plane. The path traced by a person standing at the middle point of the slipping ladder is
AnswerThe answer is (c).
As the ladder slips, the distance from the corner to its middle point stays equal to half the ladder's length, because the midpoint of the hypotenuse of a right triangle is equally far from all three vertices. So the person traces part of a circle of radius L/2 centred at the corner.
Why each option is right or wrong
- (a) The midpoint stays a fixed distance from the corner, so the path is not straight.
- (b) An ellipse is traced by a point other than the midpoint.
- (c) Correct: the path is an arc of a circle.
- (d) A parabola does not arise here.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2004, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.