1000+ Applied Mechanics and Graphic Statics MCQ for XAT [Solved]

1. Two loads of 50 kg and 75 kg are hung at the ends of a rope passing over a smooth pulley shown in below figure. The tension in the string is:
A. 50 kg
B. 75 kg
C. 25 kg
D. 60 kg
Answer : D

2. The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is ½, the velocities of separation of the balls will be equal to
A. Original velocity in the same direction
B. Half the original velocity in the same direction
C. Half the original velocity in the opposite direction
D. Original velocity in the opposite direction
Answer : D

3. 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

4. If two forces of 3 kg and 4 kg act at right angles to each other, their resultant force will be equal to
A. 7 kg
B. 1 kg
C. 5 kg
D. None of these
Answer : C

5. 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

6. Centre of gravity of a thin hollow cone lies on the axis of symmetry at a height of
A. One-half of the total height above base
B. One-third of the total height above base
C. One-fourth of the total height above base
D. None of these
Answer : B

7. A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is
A. n rpm
B. n/2 rpm
C. n/4 rpm
D. 2n rpm
Answer : B

8. A simple pendulum of length l has an energy E, when its amplitude is A. If the length of pendulum is doubled, the energy will be
A. E
B. E/2
C. 2E
D. 4E
Answer : B

9. The numbers of funicular polygons which can be drawn to pass through two specified points in the space diagram are
A. Zero
B. 1
C. 2
D. Infinity
Answer : D

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

11. If ? is the angular acceleration of a compound pendulum whose angular displacement is ?, the frequency of the motion is
A. 2? ?(?/?)
B. (1/2?) ?(?/?)
C. 4? ?(?/?)
D. 2? ?(? - ?)
Answer : B

12. 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

13. A point subjected to a number of forces will be in equilibrium, if
A. Sum of resolved parts in any two directions at right angles, are both zero
B. Algebraic sum of the forces is zero
C. Two resolved parts in any two directions at right angles are equal
D. Algebraic sum of the moments of the forces about the point is zero
Answer : A

14. The ratio of the reactions R_A and R_B of a simply supported beam shown in below figure is
A. 0.50
B. 0.40
C. 0.67
D. 1.00
Answer : D

15. A rod 5 m in length is moving in a vertical plane. When it is inclined at 60° to horizontal, its lower end is moving horizontally at 3 m/sec and upper end is moving in vertical direction. The velocity of its upper end, is
A. 0.5 m/sec
B. 1.0 m/sec
C. 1.5 m/sec
D. 2.5 m/sec
Answer : B

16. A block of weight 50 kg is placed on a horizontal plane. When a horizontal force of 18 kg is applied, the block is just on the point of motion. The angle of friction is
A. 17° 48'
B. 18° 48'
C. 19° 48'
D. 20° 48'
Answer : C

17. When a circular wheel rolls on a straight track, then the shape of body centrode and space centrode respectively are
A. Straight line and parabola
B. Straight line and circle
C. Circle and straight line
D. Circle and parabola
Answer : C

18. The unit of force in C.G.S. system of units, is called
A. Dyne
B. Newton
C. Kg
D. All the above
Answer : A

19. A weight of 100 kg is supported by a string whose ends are attached to pegs A and B at the same level shown in below figure. The tension in the string is
A. 50 kg
B. 75 kg
C. 100 kg
D. 120 kg
Answer : C

20. For the system of the loads shown in below figure, the time required for the 6.6 kg load to fall on the edge, is
A. 1 sec
B. 2 sec
C. 3 sec
D. 4 sec
Answer : C

21. 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

22. A ladder of weight 'w' rests against a smooth vertical wall, and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being 1/4. The maximum angle of inclination of the ladder to the vertical, if a man of weight 'w' is to walk to the top of it safely, is tan'1 x, where x is
A. 1/4
B. 1/3
C. 3
D. 4
Answer : B

23. The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by
A. 1 : 2
B. 1 : 1
C. 2 : 1
D. 3 : 1
Answer : D

24. The total time of collision and restitution of two bodies, is called
A. Time of collision
B. Period of collision
C. Period of impact
D. All the above
Answer : D

25. u1 and u2 are the velocities of approach of two moving bodies in the same direction and their corresponding velocities of separation are v1 and v2. As per Newton's law of collision of elastic bodies, the coefficient of restitution (e) is given by
A. e = v1 - v2/u2 - u1
B. e = u2 - u1/v1 - v2
C. e = v2 - v1/u1 - u2
D. e = v1 - v2/u2 + u1
Answer : C

26. Pick up the correct statement from the following. A rubber ball when strikes a wall rebounds but a lead ball of same mass and velocity when strikes the same wall, falls down
A. Rubber and lead balls undergo equal changes in momentum
B. Change in momentum suffered by lead ball is less that of rubber ball
C. Momentum of rubber ball is less than that of lead ball
D. None of these
Answer : D

27. For a given velocity of a projectile, the range is maximum when the angle of projection is
A. 30°
B. 45°
C. 90°
D. 0°
Answer : B

28. 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

29. Parallelogram Law of Forces states, if two forces acting simultaneously on a particle be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by
A. Its longer side
B. Its shorter side
C. The diagonal of the parallelogram which does not pass through the point of intersection of the forces
D. The diagonal of the parallelogram which passes through the point of intersection of the forces
Answer : D

30. One Newton is equivalent to
A. 1 kg. wt
B. 9.81 kg. wt
C. 981 dyne
D. 1/9.81 kg. wt
Answer : D

31. The product of mass and velocity of a moving a body, is called
A. Moment
B. Momentum
C. Power
D. Impulse
Answer : B

32. If two forces each equal to T in magnitude act at right angles, their effect may be neutralised by a third force acting along their bisector in opposite direction whose magnitude will be
A. 2 T
B. 1/2 T
C. ?2 T
D. 3 T
Answer : C

33. To avoid bending action at the base of a pier,
A. Suspension and anchor cables are kept at the same level
B. Suspension and anchor cables are fixed to pier top
C. Suspension cable and anchor cables are attached to a saddle mounted on rollers on top of the pier
D. None the these
Answer : B

34. In a simple harmonic motion, the position of equilibrium is always
A. Stable
B. Unstable
C. Neutral
D. None of the above
Answer : A

35. A vehicle weighing w kg is to run on a circular curve of radius r. If the height of its centre of gravity above the road level is h and the distance between the centres of wheels is 2a, the maximum velocity, in order to avoid over turning, will be
A. gra/h
B. ?(gra/h)
C. 3?(gra/h)
D. 4?(gra/h)
Answer : B

36. For a body moving with simple harmonic motion, the number of cycles per second, is known as its
A. Oscillation
B. Amplitude
C. Periodic time
D. Frequency
Answer : D

37. The following statement is one of the laws of Dynamic friction
A. The force of friction always acts in a direction opposite to that in which a body is moving
B. The magnitude of the kinetic friction bears a constant ratio to the normal reaction between two surfaces. The ratio being slightly less than that in the case of limiting friction
C. For moderate speeds the force of friction remains constant but decreases slightly with the increase of speed
D. All the above
Answer : D

38. Pick up the correct statement frm the following:
A. If two equal and perfectly elastic smooth spheres impinge directly, they interchange their velocities
B. If a sphere impinges directly on an equal sphere which is at rest, then a fraction ½(1 - e2) the original kinetic energy is lost by the impact
C. If two equal spheres which are perfectly elastic impinge at right angles, their direction after impact will still be at right angles
D. All the above
Answer : D

39. A light rope is loaded with many equal weights at equal horizontal intervals. The points of suspension on the rope lie on a
A. Parabola
B. Catenary
C. Cycloid
D. Ellipse
Answer : A

40. Periodic time of a particle moving with simple harmonic motion is the time taken by the particle for
A. Half oscillation
B. Quarter oscillation
C. Complete oscillation
D. None of these
Answer : C

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

42. The reaction at the support B of the beam shown in below figure is
A. 1.6 t
B. 9.6 t
C. 8.5 t
D. 0.5 t
Answer : C

43. The velocity ratio of the differential wheel and axle is
A. R/r1 - r2
B. 2R/r1
C. 3R/r1 - r2
D. 2R/r1 + r2
Answer : B

44. The C.G. of the shaded area of the below figure from the x-axis is
A. a/4
B. 3a/4
C. 3b/10
D. 3a/10
Answer : C

45. The velocity of a moving body, is
A. A vector quantity
B. A scalar quantity
C. A scalar as well as a vector quantity
D. None of these
Answer : A

46. A particle executes a simple harmonic motion. While passing through the mean position, the particle possesses
A. Maximum kinetic energy and minimum potential energy
B. Maximum kinetic energy and maximum potential energy
C. Minimum kinetic energy and maximum potential energy
D. Minimum kinetic, energy and minimum potential energy
Answer : A

47. If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is
A. Zero
B. Maximum
C. Minimum
D. None of these
Answer : B

48. 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

49. For perfectly elastic bodies, the value of coefficient of restitution is
A. Zero
B. 0.5
C. 1.0
D. Between 0 and 1
Answer : C

50. 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