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Concerned Subject (Mechanical)

Question 1Single Answer
A particle is subjected to three coplanar concurrent forces of 40 N, 50 N, and 60 N. For equilibrium, the angle between the 40 N and 50 N forces must satisfy which relation?
  1. A
    (\cos \theta = -\frac{49}{80})
  2. B
    (\cos \theta = -\frac{1}{8})
  3. C
    (\cos \theta = \frac{3}{8})
  4. D
    (\cos \theta = -\frac{5}{8})
Question 2Single Answer
A force of 100 N acts at a point whose position vector from the origin is (3\mathbf{i}+4\mathbf{j}) m. If the force is (60\mathbf{i}+80\mathbf{j}) N, what is its moment about the origin?
  1. A
    400 N·m clockwise
  2. B
    120 N·m clockwise
  3. C
    240 N·m anticlockwise
  4. D
    0 N·m
Question 3Single Answer
A smooth cylinder of weight W rests in a right-angled corner formed by a vertical wall and a horizontal floor. What are the reactions at the wall and floor respectively?
  1. A
    0 and W
  2. B
    W and W
  3. C
    (W/\sqrt{2}) and (W/\sqrt{2})
  4. D
    W and 0
Question 4Single Answer
A simply supported beam carries a central point load P. What is the maximum bending moment?
  1. A
    (PL/8)
  2. B
    (PL/16)
  3. C
    (PL/2)
  4. D
    (PL/4)
Question 5Single Answer
In a pin-jointed plane truss with j joints and m members, what condition indicates a perfect truss?
  1. A
    (m=2j-3)
  2. B
    (m=2j+3)
  3. C
    (m=j-1)
  4. D
    (m=3j-2)
Question 6Single Answer
In the method of joints, equilibrium at each joint is established using which equations?
  1. A
    (\sum M=0) only
  2. B
    (\sum F_x=0) only
  3. C
    (\sum F_x=0) and (\sum F_y=0)
  4. D
    (\sum F_y=0) and (\sum M=0)
Question 7Single Answer
Which statement is correct for a zero-force member in a truss joint having three members, two of which are collinear, with no external load at the joint?
  1. A
    Both collinear members are zero-force members
  2. B
    The longest member is unstressed
  3. C
    Every member carries equal force
  4. D
    The non-collinear member is a zero-force member
Question 8Single Answer
The principle of virtual work states that for a body in equilibrium, the total virtual work done by external forces for any compatible virtual displacement is?
  1. A
    Zero
  2. B
    Minimum
  3. C
    Maximum
  4. D
    Equal to strain energy
Question 9Single Answer
A particle moves with constant tangential acceleration. Which quantity necessarily varies linearly with time?
  1. A
    Normal acceleration
  2. B
    Radius of curvature
  3. C
    Speed
  4. D
    Angular momentum
Question 10Single Answer
For pure translation of a rigid body in plane motion, which statement is correct?
  1. A
    All points have equal angular velocity
  2. B
    One point remains stationary
  3. C
    All points move in circular paths
  4. D
    All points have equal linear velocity at an instant
Question 11Single Answer
The instantaneous centre of a body in pure translation lies?
  1. A
    At the centre of mass
  2. B
    At infinity
  3. C
    At the point of contact
  4. D
    At the origin
Question 12Single Answer
A disc rolls without slipping on a horizontal surface with centre velocity V. What is the velocity of its topmost point?
  1. A
    Zero
  2. B
    2V
  3. C
    (V/2)
  4. D
    V
Question 13Single Answer
The angular impulse of a force system about a point equals the change in?
  1. A
    Angular momentum about that point
  2. B
    Kinetic energy
  3. C
    Linear velocity
  4. D
    Potential energy
Question 14Single Answer
A body of mass m moving at velocity u is brought to rest by a constant force F. What is the stopping distance?
  1. A
    (mu/F)
  2. B
    (mu^2/F)
  3. C
    (mu^2/2F)
  4. D
    (2mu/F)
Question 15Single Answer
For a perfectly elastic direct central impact, the coefficient of restitution is?
  1. A
    0
  2. B
    0.5
  3. C
    1
  4. D
    Greater than 1
Question 16Single Answer
In a perfectly plastic collision between two particles, which quantity is conserved?
  1. A
    Linear momentum only
  2. B
    Kinetic energy only
  3. C
    Mechanical energy only
  4. D
    Relative velocity only
Question 17Single Answer
During an oblique impact between two smooth spheres, the impulse acts along?
  1. A
    The common tangent
  2. B
    The direction of initial velocity
  3. C
    The resultant velocity direction
  4. D
    The common normal at contact
Question 18Single Answer
A particle slides from rest down a smooth track through a vertical height h. Its speed at the bottom is?
  1. A
    (\sqrt{gh})
  2. B
    (2gh)
  3. C
    (\sqrt{2gh})
  4. D
    (gh/2)
Question 19Single Answer
D'Alembert's principle converts a dynamics problem into an equivalent statics problem by introducing?
  1. A
    Elastic force
  2. B
    Centrifugal force only
  3. C
    Impulsive force
  4. D
    Inertia force equal to (-m\mathbf{a})
Question 20Single Answer
The work done by centripetal force in uniform circular motion is?
  1. A
    Positive
  2. B
    Zero
  3. C
    Maximum
  4. D
    Negative
Question 21Single Answer
The mass moment of inertia of a thin circular ring of mass m and radius r about its central axis normal to the plane is?
  1. A
    (\frac{1}{4}mr^2)
  2. B
    (\frac{1}{2}mr^2)
  3. C
    (mr^2)
  4. D
    (2mr^2)
Question 22Single Answer
The mass moment of inertia of a uniform solid disc about a diameter in its plane is?
  1. A
    (\frac{1}{2}mr^2)
  2. B
    (mr^2)
  3. C
    (\frac{1}{4}mr^2)
  4. D
    (\frac{3}{4}mr^2)
Question 23Single Answer
According to the parallel-axis theorem, the moment of inertia about any axis parallel to a centroidal axis is?
  1. A
    (I_G-md^2)
  2. B
    (I_G+md)
  3. C
    (I_G/m+d^2)
  4. D
    (I_G+md^2)
Question 24Single Answer
The product of inertia of an area about two mutually perpendicular centroidal axes is zero when?
  1. A
    Neither axis is an axis of symmetry
  2. B
    At least one axis is an axis of symmetry
  3. C
    The area is triangular only
  4. D
    Both axes are inclined at 45°
Question 25Single Answer
Hooke's law is valid up to which point on the stress-strain curve?
  1. A
    Proportional limit
  2. B
    Yield point
  3. C
    Elastic limit
  4. D
    Ultimate point
Question 26Single Answer
The relationship among Young's modulus E, shear modulus G, and Poisson's ratio (\nu) is?
  1. A
    (E=G(1+\nu))
  2. B
    (E=2G(1+\nu))
  3. C
    (E=3G(1-2\nu))
  4. D
    (E=G/(1+\nu))
Question 27Single Answer
The relationship between Young's modulus E and bulk modulus K is?
  1. A
    (E=3K(1-2\nu))
  2. B
    (E=2K(1+\nu))
  3. C
    (E=K(1-\nu))
  4. D
    (E=3K(1+\nu))
Question 28Single Answer
For an incompressible isotropic material, Poisson's ratio is?
  1. A
    0
  2. B
    0.25
  3. C
    0.33
  4. D
    0.5
Question 29Single Answer
A bar of length L, area A, and modulus E is subjected to axial load P. Its strain energy is?
  1. A
    (P^2L/AE)
  2. B
    (P^2L/2AE)
  3. C
    (PL/2AE)
  4. D
    (P^2A/2EL)
Question 30Single Answer
Two bars of different materials are rigidly connected in parallel and subjected to a common axial load. Which quantity is equal in both bars?
  1. A
    Stress
  2. B
    Load
  3. C
    Strain
  4. D
    Modulus of elasticity
Question 31Single Answer
Two bars connected in series carry an axial load. Which quantity is necessarily identical in both bars?
  1. A
    Axial force
  2. B
    Stress
  3. C
    Deformation
  4. D
    Strain
Question 32Single Answer
A bar of uniform strength subjected to axial tension has cross-sectional area varying in proportion to?
  1. A
    Bending moment
  2. B
    Length squared
  3. C
    Axial force
  4. D
    Elastic modulus
Question 33Single Answer
The maximum shear stress in a state of plane stress with principal stresses (\sigma_1) and (\sigma_2) is?
  1. A
    ((\sigma_1+\sigma_2)/2)
  2. B
    (\sigma_1-\sigma_2)
  3. C
    (\sqrt{\sigma_1\sigma_2})
  4. D
    ((\sigma_1-\sigma_2)/2)
Question 34Single Answer
The centre of Mohr's circle for plane stress lies at?
  1. A
    ((\sigma_x-\sigma_y)/2)
  2. B
    ((\sigma_x+\sigma_y)/2)
  3. C
    (\tau_{xy}/2)
  4. D
    (\sigma_x+\sigma_y)
Question 35Single Answer
On a principal plane, the shear stress is?
  1. A
    Maximum
  2. B
    Minimum but non-zero
  3. C
    Zero
  4. D
    Equal to normal stress
Question 36Single Answer
The planes of maximum shear stress are inclined to the principal planes by?
  1. A
    45°
  2. B
    30°
  3. C
    60°
  4. D
    90°
Question 37Single Answer
In a state of pure shear (\tau), the principal stresses are?
  1. A
    (\tau) and 0
  2. B
    (2\tau) and (-2\tau)
  3. C
    (\tau/2) and (-\tau/2)
  4. D
    (\tau) and (-\tau)
Question 38Single Answer
For plane strain, the strain normal to the plane under consideration is?
  1. A
    Zero
  2. B
    Equal to Poisson's ratio
  3. C
    Maximum
  4. D
    Infinite
Question 39Single Answer
In a thin cylindrical pressure vessel, the hoop stress is?
  1. A
    (pd/4t)
  2. B
    (2pd/t)
  3. C
    (pd/2t)
  4. D
    (pt/2
Question 40Single Answer
The longitudinal stress in a thin closed cylindrical shell is?
  1. A
    (pd/2t)
  2. B
    (pd/t)
  3. C
    (pd/4t)
  4. D
    (pt/4
Question 41Single Answer
The hoop stress in a thin spherical pressure vessel is?
  1. A
    (pd/2t)
  2. B
    (2pd/t)
  3. C
    (pd/8t)
  4. D
    (pd/4t)
Question 42Single Answer
In a thin cylindrical pressure vessel, the ratio of hoop stress to longitudinal stress is?
  1. A
    1
  2. B
    1.5
  3. C
    2
  4. D
    4
Question 43Single Answer
According to Lame's theory for thick cylinders, the radial stress at a free outer surface is?
  1. A
    Equal to internal pressure
  2. B
    Equal to hoop stress
  3. C
    Maximum tensile stress
  4. D
    Zero
Question 44Single Answer
In a thick cylinder subjected only to internal pressure, the maximum hoop stress occurs at?
  1. A
    Outer surface
  2. B
    Mid-thickness
  3. C
    Neutral radius
  4. D
    Inner surface
Question 45Single Answer
Lame's expression for radial or hoop stress in a thick cylinder has the general form?
  1. A
    (A+Br^2)
  2. B
    (A+B/r)
  3. C
    (Ar+B/r^3)
  4. D
    (A+B/r^2)
Question 46Single Answer
Autofrettage of a thick cylinder is used primarily to?
  1. A
    Reduce its outer diameter
  2. B
    Increase thermal conductivity
  3. C
    Eliminate radial stress completely
  4. D
    Introduce beneficial residual compressive stresses near the bore
Question 47Single Answer
A beam segment over which the shear force is zero has bending moment that is?
  1. A
    Constant
  2. B
    Linearly varying
  3. C
    Parabolic
  4. D
    Cubic
Question 48Single Answer
The rate of change of bending moment with respect to beam length equals?
  1. A
    Load intensity
  2. B
    Slope
  3. C
    Deflection
  4. D
    Shear force
Question 49Single Answer
The rate of change of shear force with respect to beam length equals?
  1. A
    Negative load intensity under the usual sign convention
  2. B
    Bending moment
  3. C
    Beam slope
  4. D
    Flexural rigidity
Question 50Single Answer
At a point where shear force changes sign from positive to negative, the bending moment is generally?
  1. A
    Minimum
  2. B
    Maximum
  3. C
    Zero
  4. D
    Discontinuous
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