Question

A rod of length L is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time, when the rod makes an angle θ with horizontal the velocity of centre of mass of the rod is v₀. The velocity of the end of the rod in contact with the surface at that instant is:-

A. v₀ tanθ
B. v₀ cotθ
C. v₀cosθ
D. v₀ sinθ

Answer 1

The velocity of the end of the rod in contact with the surface is v₀ tanθ so the correct answer is A.

Step-by-step explanation:

When a rod of length L is held vertically on a smooth horizontal surface and given a gentle push at a certain angle θ with the horizontal, the velocity of the center of mass of the rod is v₀. We want to find the velocity of the end of the rod in contact with the surface at that instant.

Since the rod is held vertically, the gravitational force acts downwards on the rod. As the rod moves, this force is responsible for both the linear motion of the center of mass and the rotational motion about the contact point with the surface.

In this case, the velocity of the end of the rod in contact with the surface is v₀ tanθ, so the correct answer is A.