A rigid body in 2D equilibrium requires how many independent equations?
A One
B Two
C Three
D Six
Answer: C. Three. Planar equilibrium uses sum Fx, sum Fy and sum moments equal to zero.
A rigid body in 3D equilibrium has how many scalar equations?
A Three
B Four
C Six
D Nine
Answer: C. Six. Three force and three moment equations are available in three-dimensional statics.
A force moved to another point on a rigid body is equivalent to force plus what?
A Extra reaction only
B A mass change
C Couple moment
D A velocity change
Answer: C. Couple moment. Moving a force requires adding a couple equal to its moment about the new point.
A force’s moment vector in 3D is calculated using what?
A Position cross force
B Force dot position
C Mass times acceleration
D Velocity cross mass
Answer: A. Position cross force. The moment about a point is r cross F.
A composite-area centroid uses each part’s area and what coordinate?
A Centroid location
B Elastic modulus
C Perimeter only
D Density only
Answer: A. Centroid location. The centroid coordinate is the area-weighted average of component centroid coordinates.
If a plane area has a vertical symmetry axis, its centroid lies where?
A Outside the shape
B At every corner
C At its perimeter
D On that axis
Answer: D. On that axis. Symmetry places the centroid on the axis of symmetry.
A rectangle of width b and height h has centroidal Ix equal to what?
A h b cubed / 12
B b h cubed / 12
C b h / 2
D b squared h squared
Answer: B. b h cubed / 12. For a rectangle, the centroidal second moment about the horizontal axis is b h^3/12.
The polar area moment J about a point equals which sum?
A Ix plus Iy
B Ix minus Iy
C Ix times Iy
D Area times radius
Answer: A. Ix plus Iy. For a plane area, the polar second moment is the sum of its two perpendicular centroidal moments.
A friction angle phi is related to coefficient mu by what?
A sin phi equals mu
B tan phi equals mu
C phi equals mu squared
D cos phi equals mu
Answer: B. tan phi equals mu. The angle of friction satisfies tan phi = mu.
At impending sliding, friction magnitude is what?
A Mu times normal force
B Equal to weight always
C Zero
D Twice normal force
Answer: A. Mu times normal force. Limiting friction is F = mu N.
A rough ladder against a wall is analyzed using what conditions?
A Only vertical force balance
B Only energy balance
C Force and moment equilibrium
D Only material stress
Answer: C. Force and moment equilibrium. The ladder is a rigid body with contact reactions and must satisfy planar equilibrium.
A beam’s internal shear force is found by what method?
A Cut and equilibrium
B Area weighting
C Mass averaging
D Energy conservation only
Answer: A. Cut and equilibrium. A section cut exposes internal resultants, which are obtained from equilibrium of a segment.
A bending-moment diagram plots internal moment against what?
A Beam position
B Time
C Temperature
D Mass density
Answer: A. Beam position. The diagram shows bending moment as a function of distance along the beam.
The slope of a shear-force diagram equals distributed load with what sign convention?
A Positive load intensity always
B Negative load intensity
C Zero everywhere
D Moment divided by length
Answer: B. Negative load intensity. Under the common sign convention, dV/dx = -w.
The slope of a bending-moment diagram equals what?
A Distributed load
B Shear force
C Deflection
D Support reaction only
Answer: B. Shear force. For a beam, dM/dx equals internal shear V under the usual convention.
A simply supported beam has a pin and what other support?
A Roller
B Fixed end
C Cable only
D Free end
Answer: A. Roller. The standard simply supported beam uses a pin at one end and roller at the other.
A uniformly distributed load is replaced by a resultant at what location?
A Left support always
B Load centroid
C Right support always
D Beam centre always
Answer: B. Load centroid. The equivalent resultant acts through the centroid of the load distribution.
Virtual work for equilibrium sums forces times what?
A Actual travel time
B Material density
C Absolute temperature
D Compatible virtual displacements
Answer: D. Compatible virtual displacements. For an ideal equilibrium system, total virtual work of forces for admissible displacements is zero.
A conservative force has work independent of what?
A Initial position
B Final position
C Path taken
D Endpoint displacement
Answer: C. Path taken. Work by a conservative force depends only on initial and final states.
Stable equilibrium corresponds to a local minimum of what?
A Kinetic energy
B Friction coefficient
C Potential energy
D Reaction force
Answer: C. Potential energy. A small displacement from a stable equilibrium increases potential energy.
Mass moment of inertia depends on mass distribution about what?
A Centroid only
B Applied force
C Temperature field
D Rotation axis
Answer: D. Rotation axis. Rotational inertia reflects how mass is distributed relative to an axis.
A zero-force truss member can occur at an unloaded joint with what member pattern?
A Three collinear members
B One member only
C Four loaded members
D Two non-collinear members
Answer: D. Two non-collinear members. At an unloaded joint with two non-collinear members, both member forces are zero.
A section cut through a plane truss may solve member forces using what?
A Material testing
B Thermal strain
C Flow continuity
D Moment equilibrium
Answer: D. Moment equilibrium. The method of sections uses equilibrium of a cut portion to solve selected member forces.
A frictionless smooth contact reaction acts in which direction?
A Along the surface
B Normal to the surface
C At 45 degrees always
D Opposite the weight
Answer: B. Normal to the surface. A smooth contact cannot transmit tangential friction, so its reaction is normal.
The centroid of a semicircle lies along what?
A Its curved boundary
B Every diameter
C Outside the shape
D Symmetry axis
Answer: D. Symmetry axis. The centroid lies on the symmetry axis of the semicircular area.