UPSC Prelims 2004 Q150: Science & Technology – Physics
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
- (a) A straight line
- (b) An elliptical path
- (c) A circular path
- (d) A parabolic path
Answer: (c) A circular path
Explanation
Path of the mid-point of a slipping ladder
| Item | Result |
|---|---|
| Ladder length | L, with ends on the wall and the floor |
| Mid-point coordinates | (x/2, y/2) where x^2 + y^2 = L^2 |
| Distance of mid-point from the corner | Always L/2, a constant |
| Path | A circle (a quarter circle) of radius L/2 |
The mid-point of the slipping ladder stays at a constant distance L/2 from the corner where the wall meets the floor, so its path is a circular arc.
Answer: (c) A circular path.
Why each option is right or wrong
- (a) Incorrect. The mid-point does not move in a straight line.
- (b) Incorrect. A point at a one-third position traces an ellipse, not the mid-point.
- (c) CORRECT. The mid-point traces a quarter circle of radius L/2.
- (d) Incorrect. The path is not a parabola.
Key point
Midpoint of the hypotenuse of a right triangle is at half the hypotenuse from the right-angle vertex.
Remember
The mid-point of a sliding ladder moves on a circle.
Common mistakes
- Choosing an ellipse, which is true for other points of the ladder.
- Thinking the path is a straight line down the wall.
- Forgetting the right-angle triangle geometry.
Exam tip
Mid-point of a hypotenuse is equidistant from all three vertices.
Sources
- NCERT Class IX Mathematics — Circles
- NCERT Class XI Mathematics — Conic Sections