GATE ME 2022 Set 1 — Question 31
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+1 / -0MediumLinear & Angular Impulse-MomentumDynamicsEngineering Mechanics
Engineering Mechanics → Dynamics → Linear & Angular Impulse-Momentum
Last updated
Question
The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through O. Its mass moment of inertia is equal to about O. A point mass of hits it normally at at the location shown, and sticks to it. Immediately after the impact, the angular velocity of the rod is ___________ (in integer).
Correct answer
10 to 10
Solution
Given:
2. Final angular momentum ():
where is the combined mass moment of inertia of the rod and the point mass about O.
3. Conservation of angular momentum ():
Thus, the angular velocity of the rod immediately after impact is .
- Mass moment of inertia of the rod about O,
- Mass of the point mass,
- Velocity of the point mass,
- Distance from pivot O to the point of impact,
2. Final angular momentum ():
where is the combined mass moment of inertia of the rod and the point mass about O.
3. Conservation of angular momentum ():
Thus, the angular velocity of the rod immediately after impact is .
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Dynamics
2026 Set 1 Q16A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The…2026 Set 1 Q29A hydraulic crane supports a mass of with its piston-cylinder actuator, inclined at…2026 Set 1 Q41Two structural members are connected by a hinge and they are externally loaded as shown in the…2026 Set 1 Q48A block of kg mass is on an inclined plane. The block is connected to another hanging mass …2026 Set 1 Q50A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown…