Applied Mechanics and Graphic Statics MCQ Solved Paper for LIC AAO

1. A uniform rod 9 m long weighing 40 kg is pivoted at a point 2 m from one end where a weight of 120 kg is suspended. The required force acting at the end in a direction perpendicular to rod to keep it equilibrium, at an inclination 60° with horizontal, is
A. 40 kg
B. 60 kg
C. 10 kg
D. 100 kg
Answer : C

2. The shape of a suspended cable under its own weight, is
A. Parabolic
B. Circular
C. Catenary
D. Elliptical
Answer : C

3. ? is coefficient of friction. A wheeled vehicle travelling on a circular level track will slip and overturn simultaneously if the ratio of its wheel distance to the height of its centroid, is
A. ?
B. 2?
C. 3?
D. ½?
Answer : B

4. An ordinate in a funicular polygon represents
A. Shear force
B. Resultant force
C. Bending moment
D. Equilibrium
Answer : C

5. The motion of a particle is described by the relation x = t2- 10t + 30, where x is in metres and t in seconds. The total distance travelled by the particle from t = 0 to t = 10 seconds would be
A. Zero
B. 30 m
C. 50 m
D. 60 m
Answer : A

6. A ball which is thrown upwards, returns to the ground describing a parabolic path during its flight
A. Vertical component of velocity remains constant
B. Horizontal component of velocity remains constant
C. Speed of the ball remains constant
D. Kinetic energy of the ball remains constant
Answer : B

7. The intrinsic equation of catenary is
A. S = c tan ?
B. y = c cosh x/c
C. y = c cosh ?
D. y = c sinh ?
Answer : A

8. The velocity ratio of an inclined plane of inclination ? with horizontal for lifting a load is
A. sin ?
B. cos ?
C. tan ?
D. cosec ?
Answer : D

9. A satellite moves in its orbit around the earth due to
A. Gravitational force
B. Centripetal force
C. Centrifugal force
D. None of these
Answer : B

10. Pick up the correct statement from the following. The kinetic energy of a body
A. Before impact is equal to that after impact
B. Before impact is less than that after impact
C. Before impact is more than that after impact
D. Remain constant
Answer : C

11. Two forces of 6 Newtons and 8 Newtons which are acting at right angles to each other, will have a resultant of
A. 5 Newtons
B. 8 Newtons
C. 10 Newtons
D. 12 Newtons
Answer : C

12. When a body moves round a fixed axis, it has
A. A rotary motion
B. A circular motion
C. A translatory
D. A rotary motion and translatory motion
Answer : B

13. Pick up the incorrect statement from the following. In a simple harmonic motion
A. Velocity is maximum at its mean position
B. Velocity is minimum at the end of the stroke
C. Acceleration is minimum at the end of the stroke
D. Acceleration is zero at the mean position
Answer : C

14. Newton's law of Collision of elastic bodies states that when two moving bodies collide each other, their velocity of separation
A. Is directly proportional to their velocity of approach
B. Is inversely proportional to their velocity of approach
C. Bears a constant ratio to their velocity of approach
D. Is equal to the sum of their velocities of approach
Answer : C

15. The displacement of a particle which moves along a straight line is given by S = 4t3 + 3t2- 10 where S is in meters and t is in seconds. The time taken by the particle to acquire a velocity of 18 m/sec from rest, is
A. ½ sec
B. 1 sec
C. 1.2 sec
D. 1.5 sec
Answer : B

16. A rod AB carries three loads of 30 N, 70 N and 100 N at distances of 20 mm, 90 mm and 150 mm respectively from A. Neglecting the weight of the rod, the point at which the rod will balance is
A. 109.5 mm from A
B. 119.5 mm from A
C. 125.5 mm from A
D. 132.5 mm from A
Answer : A

17. Which one of the following laws is not applicable to a simple pendulum?
A. The time period does not depend on its magnitude
B. The time period is proportional to its length l
C. The time period is proportional to l, where l is length
D. The time period is inversely proportional to g, where g is the acceleration due to gravity
Answer : B

18. If three rigid rods are hinged together to form a triangle and are given rotary as well as translatory motion, the number of instantaneous centres of the triangle, will be
A. 1
B. 2
C. 3
D. 4
Answer : C

19. Power can be expressed as
A. Work/energy
B. Work/time
C. Work × time
D. Work/distance
Answer : B

20. The resolved part of the resultant of two forces inclined at an angle ? in a given direction is
A. Algebraic sum of the resolved parts of the forces in the direction
B. Arithmetical sum of the resolved prts of the forces in the direction
C. Difference of the forces multiplied by cosine ?°
D. Sum of the forces multiplied by the tangent ?°
Answer : A

21. The height at which the end of a rope of length l should be tied so that a man pulling at the other end may have the greatest tendency to overturn the pillar, is
A. ¾ l
B. ½ l
C. l/?2
D. 2/?3 l
Answer : C

22. The unit of moments in M.K.S system, is
A. kg.m
B. kg/m²
C. kg/sec²
D. kg/sec
Answer : A

23. A Second's pendulum gains 2 minutes a day. To make it to keep correct time its length
A. Must be decreased
B. Must be increased
C. Is not changed but weight of the bob is increased
D. Is not changed but weight of the bob is decreased
Answer : B

24. For a simple pendulum, time period for a beat, is
A. ? ?(l/g)
B. ? ?(2l/g)
C. ? ?(g/2l)
D. ? ?(l/2g)
Answer : A

25. A string of length 90 cm is fastened to two points A and B at the same level 60 cm apart. A ring weighing 120 g is slided on the string. A horizontal force P is applied to the ring such that it is in equilibrium vertically below B. The value of P is:
A. 40 g
B. 60 g
C. 80 g
D. 100 g
Answer : C

26. A particle moves in a straight line and its position is defined by the equation x = 6 t² - t³ where t is expressed in seconds and x in meters. The maximum velocity during the motion is
A. 6 m/sec
B. 12 m/sec
C. 24 m/sec
D. 48 m/sec
Answer : B

27. A particle is executing simple harmonic motion in a line 1.0 m long. If the time of one complete vibration is 1 sec, then the maximum velocity of the particle is
A. 1.00 m/sec
B. 1.57 m/sec
C. 3.14 m/sec
D. 6.28 m/sec
Answer : C

28. A smooth cylinder lying on its convex surface remains
A. In stable equilibrium
B. In unstable equilibrium
C. In neutral equilibrium
D. Out of equilibrium
Answer : B

29. The forces which meet at one point and have their lines of action in different planes are called
A. Coplanar non-concurrent forces
B. Non-coplanar concurrent forces
C. Non-coplanar non-current forces
D. Intersecting forces
Answer : B

30. For a simple pendulum, the period of one oscillation is
A. 2? ?(l/2g)
B. 2? ?(2g/l)
C. 2? ?(l/g)
D. 2? ?(g/2l)
Answer : C

31. The Law of Polygon of Forces states that
A. If a polygon representing the forces acting at point in a body is closed, the forces are in equilibrium
B. If forces acting on a point can be represented in magnitude and direction by the sides of a polygon taken in order, then the resultant of the forces will be represented in magnitude and direction by the closing side of the polygon
C. If forces acting on a point can be represented of a polygon taken in order, their sides of a polygon taken in order, their resultant will be represented in magnitude and direction by the closing side of the polygon, taken in opposite order
D. If forces acting on a point can be represented in magnitude and direction by the sides of a polygon in order, the forces are in equilibrium
Answer : C

32. The centre of gravity of a triangle is at the point where three
A. Medians of the triangle meet
B. Perpendicular bisectors of the sides of the triangle meet
C. Bisectors of the angle of the triangle meet
D. None of these
Answer : A

33. If two forces acting at a point are in equilibrium, they must be equal in magnitude and their line of action must be along
A. The same line in the same sense
B. The same line in opposite sense
C. The perpendicular to both the lines
D. None of these
Answer : B

34. A cube on a smooth horizontal surface
A. Cannot be in stable equilibrium
B. Cannot be in neutral equilibrium
C. Cannot be in unstable equilibrium
D. Can be in any of these states
Answer : D

35. A heavy ladder resting on a floor and against a vertical wall may not be in equilibrium, if
A. Floor is smooth and the wall is rough
B. Floor is rough and the wall is smooth
C. Floor and wall both are smooth surfaces
D. Floor and wall both are rough surfaces
Answer : C

36. If a ball which is dropped from a height of 2.25 m on a smooth floor attains the height of bounce equal to 1.00 m, the coefficient of the restitution between the ball and floor, is
A. 0.25
B. 0.50
C. 0.67
D. 0.33
Answer : B

37. The centre of gravity of a quadrant of a circle lies along its central radius at a distance of
A. 0.2 R
B. 0.4 R
C. 0.3 R
D. 0.6 R
Answer : D

38. A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The mechanical advantage of the lifting machine is
A. 15
B. 18
C. 20
D. 26
Answer : C

39. In a simple screw jack, the pitch of the screw is 9 mm and length of the handle operating the screw is 45 cm. The velocity ratio of the system is
A. 1.5
B. 5
C. 25
D. 314
Answer : D

40. A number of forces acting simultaneously on a particle of a body
A. May not be replaced by a single force
B. May be replaced by a single force
C. May be replaced by a single force through C.G. of the body
D. May be replaced by a couple
Answer : B

41. Kinetic friction may be defined as
A. Friction force acting when the body is just about to move
B. Friction force acting when the body is in motion
C. Angle between normal reaction and resultant of normal reaction and limiting friction
D. Ratio of limiting friction and normal reaction
Answer : B

42. If G is the Gauge of track, v is velocity of the moving vehicle, g is the acceleration due to gravity and r is the radius of a circular path, the required super elevation is
A. gv²/Gr
B. Gr²/gr
C. Gr²/gv²
D. Gv²/gv
Answer : D

43. The resultant of two forces acting at right angles is 5 kgf and if they act at an angle of 60°, it is 37 kgf. The magnitudes of the forces are:
A. 2 kgf, 3 kgf
B. 3 kgf, 4 kgf
C. 4 kgf, 5 kgf
D. 5 kgf, 3 kgf
Answer : B

44. If a set of given forces are such that their free vectors build a closed polygon, then
A. The resultant force and resultant couple are always zero
B. The resultant force is zero but resultant couple is not zero
C. The resultant force is zero but resultant couple may not be zero
D. The resultant force and resultant couple both may not be zero
Answer : C

45. Maximum efficiency of a screw jack for the angle of friction ?, is
A. sin ?/(1 + sin ?)
B. (1 - sin ?)/sin ?
C. (1 + sin ?)/(1 - sin ?)
D. (1 - sin ?)/(1 + sin ?)
Answer : D

46. The equation of motion of a particle starting from rest along a straight line is x = t³ - 3t²+ 5. The ratio of the accelerations after 5 sec and 3 sec will be
A. 2
B. 3
C. 4
D. 5
Answer : @

47. Two objects moving with uniform speeds are 5 m apart after 1 second when they move towards each other and are 1 m apart when they move in the same direction. The speeds of the objects are
A. 2 m/sec and 2 m/sec
B. 3 m/sec and 2 m/sec
C. 3 m/sec and 3 m/sec
D. 4 m/sec and 6 m/sec
Answer : B

48. The characteristic of a couple is:
A. Algebraic sum of forces, constituting a couple is zero
B. Algebraic sum of moments of forces, constituting a couple, about any point, is same
C. A couple can be never the balanced by a single force
D. All the above
Answer : D

49. The acceleration of a particle moving along the circumference of a circle with a uniform speed, is directed
A. Radially
B. Tangentially at that point
C. Away from the centre
D. Towards the centre
Answer : B

50. A retarding force on a body does not
A. Change the motion of the body
B. Retard the motion of the body
C. Introduce the motion of the body
D. None of these
Answer : B