A rod AB is moving on a fixed circle of radius R with constant velocity ‘ v ’ as shown in figure. P is the point of intersection of the rod and the circle. At an instant the rod is at a distance x = 
from center of the circle. The velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
V P = 
V
ω = 
= 
Sol.
As a rod AB moves, the point ‘ P ’ will always lie on the circle.
∴ its velocity will be along the circle as shown by ‘ V P ’ in the figure.
If the point P has to lie on the rod ‘ AB ’ also then it should have
component in ‘ x ’ direction as ‘ V ’ .
∴ V P sin θ = V ⇒ V P = V cosec θ
here cos θ = 
= 
. 
= 
∴ sin θ = ∴ cosec θ =
∴ V P = 
V ..Ans.
Sol. ω = 
= 
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