Question

A rod of length $2l$ is moving such that its ends A and B move in contact with the horizontal floor and vertical wall respectively as shown in figure. O is the intersection point of the vertical wall and horizontal floor. The velocity vector of the center of rod C is always directed along tangent drawn at C to the:

• A. circle of radius $\frac{l}{2}$ whose centre lies at O
• B. circle of radius $l$ whose centre lies at O
• C. circle of radius $2l$ whose centre lies at O
• D. None of these

Answer 1

Answer: (B)

circle of radius $l$ whose centre lies at O

A rod of length
At any instant of time the rod makes an angle $\theta$ with
horizontal, the x & y coordinates of centre of rod are
$x=lcos\theta$, y $=lsin\theta$
$x^2+y^2=l^2$
Hence the centre C moves along a circle of radius with
centre at O.
$\therefore$ velocity vector of C is always directed along the tangent drawn at C to the circle of radius l whose centre lies at O.