Question

A rigid rod leans against a vertical wall (y-axis) as shown in figure. The other end of the rod is on the horizontal floor. Point A is pushed downwards with constant velocity. Path of the centre of the rod is –

• A. A straight line passing through origin
• B. A straight line not passing through origin
• C. A circle of radius l/2 and centre at origin
• D. A circle of radius l/2 but centre not at origin

Answer 1

Answer: (C)

A circle of radius l/2 and centre at origin

Answer 2

Let l be the length of the rod and q the angle of rod with x-axis (horizontal) at some instant of time. Co-ordinates of the centre of rod at this instant of time are

x =$\frac{l}{2}$cos q

and y =$\frac{l}{2}$sin q

Squaring and adding Eqs. (1) and (2), we get:

x² + y² =$\frac{l^{2}}{4}$

Which is an equation of a circle of radius $\frac{l}{2}$ and centre at origin.