GATE ME 2022 Set 2 — Question 37
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67HardLinear & Angular Impulse-MomentumDynamicsEngineering Mechanics
Engineering Mechanics → Dynamics → Linear & Angular Impulse-Momentum
Last updated
Question
A rigid homogeneous uniform block of mass 1 kg, height m and width m is pinned at one corner and placed upright in a uniform gravitational field ( m/s), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force , producing an impulse , is applied at a height of m from the bottom as shown. Assume all joints to be frictionless. The minimum value of required to topple the block is
Correct answer
(A) 0.953 Ns
Solution
To topple the block, it must rotate about the pin until its center of gravity (CG) is vertically above the pin. The energy required for this is the change in potential energy.
Distance from pin to CG: m.
Height of CG at the toppling point (vertically above pin): m.
Initial kinetic energy after impulse: .
1.Calculate the moment of inertia () about the pin:
For a rectangular block rotating about a corner:2.Calculate the required potential energy change ():
Initial height of CG: m.Distance from pin to CG: m.
Height of CG at the toppling point (vertically above pin): m.
3.Relate the impulse () to initial kinetic energy ():
Angular impulse about the pin: .Initial kinetic energy after impulse: .
4.Equate and for minimum impulse:
Thus, the correct option is (A).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…