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 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
Show Hint
For rigid rotation, relate angular speed using v=ω r.
Updated On: Mar 20, 2026
- \(\dfrac{v_0}{r}\)
- \(\dfrac{v_0}{2r}\)
- \(\dfrac{2v_0}{r}\)
- v₀ r
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
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)
Was this answer helpful?
0
0
Top BITSAT Physics Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions
Top BITSAT Rotational motion Questions
- A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc -
- A solid sphere of mass 2 kg and radius 0.5 m rolls without slipping down an inclined plane of height 3 m. What is its speed at the bottom? (Take \( g = 9.8\, \text{m/s}^2 \))
- A disc of moment of inertia \( I \) is rotating with angular velocity \( \omega \). A ring of the same mass and radius, initially at rest, is gently placed coaxially on top of the disc. What is the final angular velocity of the system?
- The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is
- A constant torque of 31.4 N-m is exerted on a pivoted wheel. If angular acceleration of wheel is 4 rad s⁻², then the moment of inertia of the wheel is:
View More Questions
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions