60 solved GATE ME questions on Engineering Mechanics, drawn from 11 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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Identify the system, isolate it, and label every external force and moment before applying equilibrium or Newton's laws. These selected foundations cover statics and dynamics of particles and rigid bodies. They are not a complete syllabus; friction, virtual work, and 3D problems need separate study.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
Isolate the body and replace every contact with the force or moment it applies. For static equilibrium of a planar rigid body, ΣFₓ = 0, ΣFᵧ = 0, and ΣM about any point = 0. Three equations determine at most three unknowns; more supports make the problem statically indeterminate.
Check yourself: Have you included all reaction forces and chosen a convenient moment center?
Static friction satisfies f ≤ μₛN. At impending slip, f = μₛN with direction opposing the tendency to move. Kinetic friction uses f = μₖN once sliding begins. A friction force does not always equal μN; it adjusts to maintain equilibrium until the limit is reached.
Check yourself: Is the body actually on the verge of slipping, or is friction below its limit?
Position, velocity, and acceleration are related by differentiation: v = ds/dt, a = dv/dt. For constant acceleration, v = v₀ + at and s = s₀ + v₀t + ½at². For curvilinear motion, resolve into tangential (speed change) and normal (direction change) components: aₜ = dv/dt, aₙ = v²/r.
Check yourself: Have you used a consistent sign convention for displacement and acceleration?
ΣF = ma applies to each particle or to the mass center of a system. For a system of particles, internal forces cancel in pairs. Weight acts at the center of gravity. For rigid-body plane motion, additionally ΣM_G = I_G α about the mass center or ΣM_O = I_O α about a fixed point O.
Check yourself: Is the reference point for moments either the mass center or a fixed point?
The work-energy theorem states: net work = ΔKE. Potential energy from gravity is mgh. Impulse equals change in momentum: ∫F dt = Δ(mv). For collisions, the coefficient of restitution e relates separation speed to approach speed along the line of impact. Momentum is conserved when external impulse is negligible.
Check yourself: Have you included work done by all forces, including friction and gravity?
Original teaching example · not a PYQ
Original example: a 10 kg block rests on a horizontal surface with μₛ = 0.4. A horizontal force P is applied. Assume g = 10 m/s² and the block is a particle. Find the minimum P to initiate sliding.
Minimum P = 40 N to initiate sliding.
A 2 kg particle starts from rest and slides 5 m down a smooth (frictionless) incline at 30° to the horizontal. Assume g = 10 m/s². Find the speed at the bottom using work-energy methods.
Speed at the bottom = √50 ≈ 7.07 m/s.
Height drop h = 5 sin 30° = 2.5 m. Work by gravity = mgh = 2 x 10 x 2.5 = 50 J. With no friction, net work = 50 J = ½mv². So v² = 2 x 50/2 = 50, giving v = √50 ≈ 7.07 m/s.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental lecture notes and problems on forces, equilibrium, and structural analysis. Pair with dynamics resources for full coverage of engineering mechanics.
Free supplemental course covering kinematics, Newton's laws, energy methods, and momentum for particles and rigid bodies.
This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE ME papers. Questions can carry more than one subject tag; counts are not marks weightage.
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