Engineering Mechanics and Dynamics MCQs 2026

A body is in static equilibrium when the resultant of all forces and all moments acting on it is

1. A infinite ✓
2. B equal to its weight only ✓
3. C equal to friction force only ✓
4. D zero ✓

According to Newton's first law, a particle continues in its state of rest or uniform motion unless acted upon by

1. A gravity alone always ✓
2. B internal stress only ✓
3. C an unbalanced external force ✓
4. D centripetal acceleration only ✓

Newton's second law in vector form is stated as

1. A F = mv ✓
2. B F = m/a ✓
3. C F = m + a ✓
4. D F = ma ✓

The unit of force in SI system is

1. A joule ✓
2. B watt ✓
3. C newton ✓
4. D pascal ✓

For a rigid body in plane motion, the number of independent equations of equilibrium is

1. A two ✓
2. B six ✓
3. C one ✓
4. D three ✓

The moment of a force about a point equals

1. A force times total distance along action line ✓
2. B force divided by distance ✓
3. C force times angle only ✓
4. D force times perpendicular distance from point to line of action ✓

Varignon's theorem states that the moment of a force about a point equals

1. A the sum of moments of its components about the same point ✓
2. B the product of components only ✓
3. C zero always for concurrent forces ✓
4. D the moment of resultant only about another point ✓

The coefficient of static friction μs is defined as the ratio of

1. A kinetic friction to velocity ✓
2. B normal force to weight always ✓
3. C limiting friction to normal reaction ✓
4. D applied force to acceleration ✓

Angle of friction φ is related to coefficient of friction μ by

1. A tan φ = μ ✓
2. B sin φ = μ ✓
3. C cos φ = μ ✓
4. D φ = μ in degrees ✓

Wedge friction problems are solved using

1. A only energy methods always ✓
2. B Bernoulli equation ✓
3. C Fourier law ✓
4. D equilibrium equations including friction on sliding surfaces ✓

Work done by a constant force moving through displacement s along its line of action is

1. A F/s ✓
2. B F s cos 90° only always ✓
3. C m g h only ✓
4. D F s ✓

Kinetic energy of a particle of mass m moving with speed v is

1. A ½ m v² ✓
2. B m v ✓
3. C m v² ✓
4. D 2 m v² ✓

Work-energy principle states that work done by all forces equals

1. A change in kinetic energy ✓
2. B change in potential energy only ✓
3. C zero always ✓
4. D change in momentum only ✓

Potential energy of a weight W raised through height h is

1. A W/h ✓
2. B ½ W h² ✓
3. C W h² ✓
4. D W h ✓

Conservation of mechanical energy applies when

1. A only conservative forces do work ✓
2. B friction is always present ✓
3. C external impulses act ✓
4. D mass varies with time ✓

Linear impulse is defined as

1. A integral of force over time interval ✓
2. B force times distance only ✓
3. C mass times velocity squared ✓
4. D moment of inertia times angular speed ✓

Impulse-momentum equation for a particle is

1. A J = ½ m v² ✓
2. B J = m(v₂ − v₁) ✓
3. C J = F d only always ✓
4. D J = I ω ✓

Coefficient of restitution e for direct impact is

1. A ratio of masses ✓
2. B ratio of contact forces ✓
3. C ratio of relative speed of separation to relative speed of approach ✓
4. D always equal to 1 ✓

For a projectile neglecting air resistance, horizontal component of velocity

1. A remains constant ✓
2. B increases linearly with time ✓
3. C decreases to zero at apex only ✓
4. D equals vertical component always ✓

Maximum height of a projectile launched vertically upward with speed u is

1. A u/g ✓
2. B u²/(2g) ✓
3. C 2u/g ✓
4. D u²/g ✓

Time of flight for projectile launched and landing at same level with speed u at angle θ is

1. A u sin θ / g ✓
2. B u cos θ / g ✓
3. C 2u cos θ / g ✓
4. D 2u sin θ / g ✓

Range of projectile on level ground is maximum when launch angle is

1. A 45° ✓
2. B 30° ✓
3. C 60° ✓
4. D 90° ✓

Relative velocity of A with respect to B is given by

1. A v_A − v_B ✓
2. B v_A + v_B ✓
3. C v_B − v_A only when parallel ✓
4. D v_A × v_B ✓

In river-boat problems, minimum time crossing requires boat velocity

1. A parallel to river bank always ✓
2. B opposite to current only ✓
3. C perpendicular to river flow relative to water ✓
4. D zero relative to ground ✓

Centripetal acceleration of a particle in circular motion of radius r at speed v is

1. A v r toward center ✓
2. B r/v² outward ✓
3. C v²/r directed toward center ✓
4. D v/r tangential ✓

Centrifugal force in a rotating frame is

1. A a fictitious outward force equal to m ω² r ✓
2. B a real force toward center ✓
3. C equal to gravitational force always ✓
4. D zero in inertial frame ✓

Belt friction equation T₂/T₁ = e^(μθ) is valid when

1. A belt is on verge of slipping over a fixed drum ✓
2. B belt moves without friction ✓
3. C angle θ is in degrees without conversion ✓
4. D tension is zero ✓

Mass moment of inertia of a thin rod of mass M and length L about center is

1. A ML²/3 ✓
2. B ML²/2 ✓
3. C ML²/12 ✓
4. D M L ✓

Parallel axis theorem states I = I_c +

1. A M d ✓
2. B M d² ✓
3. C M d³ ✓
4. D d² only ✓

Radius of gyration k is defined by

1. A I = k/M ✓
2. B I = M k² ✓
3. C k = I M ✓
4. D k = √M/I ✓

D'Alembert's principle converts a dynamics problem into

1. A an equivalent static equilibrium by adding inertia forces ✓
2. B a thermodynamic cycle analysis ✓
3. C a heat transfer problem ✓
4. D a fluid statics problem only ✓

Coriolis acceleration in a rotating frame is proportional to

1. A ω² r only ✓
2. B v_rel only ✓
3. C g always ✓
4. D 2 ω × v_rel ✓

Lami's theorem applies to

1. A any number of non-concurrent forces ✓
2. B only frictionless contacts ✓
3. C three concurrent coplanar forces in equilibrium ✓
4. D only dynamic impact problems ✓

The resultant of two equal forces P each acting at angle θ between them has magnitude

1. A 2P sin(θ/2) ✓
2. B 2P cos(θ/2) ✓
3. C P cos θ ✓
4. D 2P ✓

A couple produces

1. A translation without rotation ✓
2. B pure rotation without translation ✓
3. C zero moment about any point ✓
4. D only normal stress in bodies ✓

Kinetic friction is generally

1. A less than limiting static friction ✓
2. B greater than static friction ✓
3. C equal to normal force ✓
4. D independent of surfaces ✓

Power is defined as

1. A product of mass and velocity ✓
2. B force times time only ✓
3. C momentum per unit volume ✓
4. D rate of doing work ✓

Angular momentum of a particle about point O is

1. A m v only ✓
2. B I ω only always ✓
3. C r × (m v) ✓
4. D F × t ✓

For central force motion, which quantity is conserved

1. A angular momentum about force center ✓
2. B linear momentum always ✓
3. C kinetic energy always ✓
4. D potential energy always in all cases ✓

Banked curve without friction at design speed relies on

1. A weight component only ✓
2. B engine thrust ✓
3. C normal reaction component toward center providing centripetal force ✓
4. D Coriolis force ✓

Instant center of rotation for a body in plane motion is

1. A center of mass always ✓
2. B center of gravity only for static bodies ✓
3. C any point on the body always ✓
4. D point with zero velocity in that instant ✓

Rolling without slipping condition relates linear and angular speed by

1. A v = ω r ✓
2. B v = ω/r ✓
3. C v = ω r² ✓
4. D v = ω only ✓

Moment of inertia of a solid sphere about diameter is

1. A 2/3 M R² ✓
2. B M R² ✓
3. C 2/5 M R² ✓
4. D 4/3 M R² ✓

Principle of transmissibility of force states

1. A force can be moved anywhere freely ✓
2. B force may be moved along its line of action without changing external effects on rigid body ✓
3. C force must always act at centroid ✓
4. D force direction may change freely ✓

A truss with all two-force members analyzed by method of joints assumes

1. A loads at joints and negligible member weight ✓
2. B distributed loading on each member always ✓
3. C plastic deformation in joints ✓
4. D dynamic impact loading ✓

Three-force member in equilibrium has lines of action that

1. A must always be perpendicular ✓
2. B must be concurrent or parallel ✓
3. C must pass through center of mass only ✓
4. D are unrelated ✓

Efficiency of a screw jack neglecting collar friction is approximately

1. A cos α only ✓
2. B μ only without angle ✓
3. C tan(α)/tan(α+φ) where α is thread lead angle ✓
4. D always 100% ✓

Collision is perfectly elastic when coefficient of restitution is

1. A 0 ✓
2. B 0.5 always ✓
3. C infinity ✓
4. D 1 ✓

A body sliding down rough incline of angle θ with coefficient μ accelerates if

1. A μ > tan θ ✓
2. B tan θ > μ ✓
3. C θ = 0 always ✓
4. D μ = 1 always ✓

Conical pendulum period depends on

1. A bob mass only ✓
2. B air density only ✓
3. C string thickness only ✓
4. D length and angle of string, not bob mass ✓

The impulse required to stop a moving body equals

1. A its kinetic energy ✓
2. B its initial momentum ✓
3. C its weight ✓
4. D half its momentum ✓

For a particle in SHM, acceleration is proportional to

1. A velocity ✓
2. B time squared ✓
3. C negative displacement from mean position ✓
4. D constant value always ✓

Work done by friction on a sliding block is generally

1. A always positive ✓
2. B negative ✓
3. C zero always ✓
4. D equal to normal force ✓

Mechanical advantage of ideal machine equals

1. A input work divided by output work ✓
2. B velocity ratio only without efficiency ✓
3. C always less than 1 ✓
4. D output force divided by input force ✓

Velocity ratio of belt drive equals

1. A always 1 ✓
2. B tension ratio T2/T1 ✓
3. C coefficient of friction only ✓
4. D ratio of driven pulley diameter to driver pulley diameter for speed of driven ✓

Creep in belt drive refers to

1. A elastic stretching only without slip ✓
2. B slight relative sliding due to tension difference over arc of contact ✓
3. C thermal expansion of belt only ✓
4. D centrifugal force only ✓

Product of inertia I_xy for an area is zero when

1. A area is any triangle always ✓
2. B area is unsymmetrical always ✓
3. C centroid is at origin only ✓
4. D x or y axis is axis of symmetry ✓

Polar moment of inertia J for solid circular shaft equals

1. A π d²/4 ✓
2. B π d⁴/32 ✓
3. C π d³/16 ✓
4. D bh³/12 ✓

A body in limiting equilibrium on horizontal plane has friction force equal to

1. A mg always regardless of applied force ✓
2. B zero ✓
3. C μ N ✓
4. D applied horizontal force always even below limit ✓

Newton's third law states that action and reaction forces

1. A cancel on same body always ✓
2. B act on same body ✓
3. C need not be collinear ✓
4. D are equal, opposite, and act on different bodies ✓

Resultant of concurrent forces found by polygon method uses

1. A scalar addition of magnitudes only ✓
2. B head-to-tail vector addition ✓
3. C cross product only ✓
4. D only graphical moment method ✓

For a lift accelerating upward, apparent weight of passenger equals

1. A m(g − a) ✓
2. B mg always ✓
3. C m(g + a) ✓
4. D zero ✓

At the top of vertical loop, minimum speed to maintain contact is

1. A gr ✓
2. B √(g r) ✓
3. C g/r ✓
4. D zero ✓

Relative acceleration in general plane motion includes

1. A translation of reference plus rotational component ✓
2. B only centripetal term always ✓
3. C only Coriolis in inertial frame ✓
4. D zero if speeds equal ✓

The principle of virtual work for ideal systems in equilibrium states Σ(δW)=0 for

1. A virtual displacements consistent with constraints ✓
2. B actual displacements only with friction doing work ✓
3. C any displacement violating constraints ✓
4. D only dynamic motion ✓

A force system reducible to a couple and single force not through that couple's axis has

1. A pure couple only always ✓
2. B zero resultant always ✓
3. C only scalar resultant ✓
4. D a wrench (force-couple system) ✓

Dynamic equilibrium using D'Alembert includes inertia torque for rotation as

1. A I α added as real torque ✓
2. B zero always ✓
3. C m a only ✓
4. D −I α ✓

For projectile at maximum range on level ground, sin 2θ equals

1. A 0 ✓
2. B 0.5 ✓
3. C 1 ✓
4. D 2 ✓

Sliding velocity in belt friction problem affects

1. A nothing in capstan equation ✓
2. B only mass moment of inertia ✓
3. C direction of impending slip determining which tension is larger ✓
4. D only gravitational potential ✓

The kinetic energy of a rigid body rotating about fixed axis is

1. A ½ m v² only ✓
2. B ½ I ω² ✓
3. C I ω ✓
4. D m g h ✓

Linear momentum of a system is conserved when

1. A internal forces are zero only ✓
2. B net external force is zero ✓
3. C friction always present ✓
4. D energy is not conserved ✓

Friction angle on inclined plane at which body is on verge of sliding down equals inclination when

1. A always 45° ✓
2. B tan θ = μ ✓
3. C μ = 0 always ✓
4. D θ = 90° minus μ ✓

Centrifugal force magnitude on mass m at radius r with angular speed ω is

1. A m ω r ✓
2. B m ω/r ✓
3. C m g ✓
4. D m ω² r ✓

Coriolis effect deflects moving objects on rotating earth because of

1. A magnetic field only ✓
2. B rotation of reference frame ✓
3. C gravity variation only ✓
4. D air viscosity only ✓

Work done by internal forces in a rigid body is

1. A zero for rigid idealization ✓
2. B always equal to KE change alone ✓
3. C always positive ✓
4. D equal to impulse ✓

Instantaneous center for a wheel rolling on ground lies at

1. A center of wheel always ✓
2. B top of wheel ✓
3. C contact point with ground ✓
4. D infinity always ✓

A particle moving with constant speed in a circle has

1. A zero centripetal acceleration ✓
2. B zero tangential acceleration ✓
3. C zero velocity ✓
4. D zero angular speed ✓

The principle of conservation of angular momentum applies when

1. A any internal moment exists ✓
2. B linear momentum is not conserved ✓
3. C net external moment about axis is zero ✓
4. D only in statics ✓

For two blocks connected by string over frictionless pulley (Atwood), acceleration equals

1. A g(m1−m2)/(m1+m2) ✓
2. B g always ✓
3. C zero always ✓
4. D g(m1+m2)/(m1−m2) ✓

Limiting friction is independent of

1. A normal force ✓
2. B surface materials ✓
3. C apparent area of contact for rigid bodies per Amontons-Coulomb law ✓
4. D roughness through μ ✓

The moment of a couple is measured in

1. A N·m same as moment of force ✓
2. B N/m ✓
3. C N·m² ✓
4. D joule only never N·m ✓

If resultant force on a particle is zero, particle

1. A must be at rest always ✓
2. B remains at rest or moves with constant velocity ✓
3. C must accelerate ✓
4. D must move in circle ✓

Energy lost in partially inelastic impact appears mainly as

1. A deformation and heat ✓
2. B increase in total momentum ✓
3. C increase in angular momentum always ✓
4. D gravitational PE only ✓

Belt tension on slack side is lower because

1. A centrifugal force zero always ✓
2. B pulley mass reduces tension ✓
3. C friction over wrap angle transfers force from driver ✓
4. D gravity alone increases tight side ✓

Mass moment of inertia of thin ring about central axis is

1. A ½ M R² ✓
2. B M R² ✓
3. C 2/5 M R² ✓
4. D M R ✓

D'Alembert inertia force acts

1. A same as acceleration ✓
2. B always vertical downward ✓
3. C opposite to acceleration direction through mass center ✓
4. D only in rotating frames ✓

Relative motion analysis in mechanisms commonly uses

1. A only thermodynamic charts ✓
2. B Mohr circle only ✓
3. C steam tables only ✓
4. D velocity and acceleration polygons or vector equations ✓

For a particle under uniform gravitational field, trajectory in vacuum is

1. A circular always ✓
2. B parabolic ✓
3. C straight line always ✓
4. D hyperbolic always ✓

Magnitude of cross product |a × b| equals

1. A a b sin θ ✓
2. B a b cos θ ✓
3. C a + b ✓
4. D a b ✓

Dot product of two perpendicular vectors is

1. A one ✓
2. B product of magnitudes ✓
3. C negative one always ✓
4. D zero ✓