Question

A thin but rigid semicircular wire frame of radius r is hinged at O and can rotate in its own vertical plane. A smooth peg P starts from O and moves horizontally with constant speed v₀, lifting the frame upwards as shown in the figure. Find the angular velocity ω of the frame when its diameter makes an angle of 60^∘ with the vertical. \includegraphics[width=0.5\linewidth]34.png

• A. \(\dfrac{v_0}{r}\)
• B. \(\dfrac{v_0}{2r}\)
• C. \(\dfrac{2v_0}{r}\)
• D. v₀ r

Hint:

For rigid rotation, relate angular speed using v=ω r.

Answer 1

The Correct Option is A

Step 1: The peg constrains the end of the diameter to move horizontally with speed v₀.
Step 2: Linear speed of that point is related to angular speed: v = ω r
Step 3: Hence ω = (v₀)/(r)