Applied Mechanics and Graphic Statics MCQ Solved Paper for RRB Group D

1. 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

2. The units of moment of inertia of an area are
A. kg/m
B. kg/m²
C. m⁴
D. m³
Answer : C

3. The C.G. of a thin hollow cone of height h, above its base lies on the axis, at a height of
A. h/3
B. h/4
C. 2h/3
D. 3h/4
Answer : C

4. A ball moving on a smooth horizontal table hits a rough vertical wall, the coefficient of restitution between ball and wall being 1/3. The ball rebounds at the same angle. The fraction of its kinetic energy lost is
A. 1/3
B. 2/3
C. 1/9
D. 8/9
Answer : D

5. 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

6. A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its centre of mass has a speed of 200 mm/sec. The work required to stop the hoop is
A. 2 J
B. 4 J
C. 6 J
D. 8 J
Answer : B

7. 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

8. If ? and u are angle of projection and initial velocity of a projectile respectively, the total time of flight, is given by
A. T = u sin 2?/g
B. T = u sin²?/g
C. T = u sin²?/2g
D. T = 2u sin?/g
Answer : D

9. The load shared by the member BC of the structure shown in below figure is

A. 23 t
B. 32 t
C. 4 t
D. 3 t
Answer : C

10. 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

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

12. The gravitational force makes a satellite go round the earth in a circular orbit, if it is projected with an initial velocity of
A. 8.04 km/sec at a height of 285 km
B. 11.11 km/sec at a height of 37,400 km
C. 11.26 km/sec, the satellite escapes the pull of the earth
D. All the above
Answer : D

13. The moment of inertia of a hollow circular section whose external diameter is 8 cm and internal diameter is 6 cm, about centroidal axis, is
A. 437.5 cm⁴
B. 337.5 cm⁴
C. 237.5 cm⁴
D. 137.5 cm⁴
Answer : D

14. 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

15. The angles between two forces to make their resultant a minimum and a maximum respectively are
A. 0° and 90°
B. 180° and 90°
C. 90° and 180°
D. 180° and 0°
Answer : D

16. 0.For maximum range of a projectile, the angle of projection should be
A. 30°
B. 45°
C. 60°
D. None of these
Answer : B

17. ? 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

18. 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

19. In the structure shown in below figure, the member which carries zero force, is
A. AB
B. BC
C. BE
D. All the above
Answer : D

20. The rotational velocity of a satellite is increased by 450 m per second if its launch is done from equator
A. Eastward
B. Northward
C. Westward
D. Southward
Answer : A

21. Two parallel forces 20 kg and 15 kg act. In order tat the distance of the resultant from 20 kg force may be the same as that of the former resultant was from 15 kg, the 20 kg force is diminished by
A. 5.5 kg
B. 6.25 kg
C. 8.75 kg
D. 10.5 kg
Answer : C

22. The tension in a cable supporting a lift
A. Is more when the lift is moving downwards
B. Is less when the lift is moving upwards
C. Remains constant whether its moves downwards or upwards
D. Is less when the lift is moving downwards
Answer : D

23. 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

24. Engineer's units of force, is
A. Newton in absolute units
B. Dyne in absolute units
C. Newton and dyne in absolute units
D. All the above
Answer : A

25. Two shots fired simultaneously from the top and bottom of a vertical tower with elevations of 30° and 45° respectively strike a target simultaneously. If horizontal distance of the target from the tower is 1000 m, the height of the tower is
A. 350 m
B. 375 m
C. 400 m
D. 425 m
Answer : D

26. Two particles have been projected at angles 64° and 45° to the horizontal. If the velocity of projection of first is 10 m/sec, the velocity of projection of the other for equal horizontal ranges is
A. 9.3 m/sec
B. 8.3 m/sec
C. 7.3 m/sec
D. 6.3 m/sec
Answer : A

27. 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

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

29. If the angular distance, 0 = 2t³ - 3t², the angular acceleration at t = 1 sec. is
A. 1 rad/sec²
B. 4 rad/sec²
C. 6 rad/sec²
D. 12 rad/sec²
Answer : C

30. The units of inertia of mass are
A. kg/m
B. kg/m²
C. m⁴
D. kg-m²
Answer : D

31. If the kinetic energy and potential energy of a simple harmonic oscillator of amplitude A are both equal to half the total energy, then the displacement is equal to
A. A
B. A/2
C. A/?2
D. A?2
Answer : C

32. The necessary condition of equilibrium of a body is:
A. Algebraic sum of horizontal components of all the forces must be zero
B. Algebraic sum of vertical components of all the forces must be zero
C. Algebraic sum of the moments of the forces about a point must be zero
D. All (a), (b) and (c)
Answer : D

33. 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

34. The unit of impulse, is
A. kg.m/sec
B. kg.m/sec
C. kg.m/sec²
D. kg.m/sec
Answer : A

35. The locus of the instantaneous centre of a moving rigid body, is
A. Straight line
B. Involute
C. Centroid
D. Spiral
Answer : C

36. For a self-locking machine, the efficiency should be
A. Less than 60%
B. 50 %
C. More than 50%
D. None of these
Answer : A

37. One Newton is equivalent to
A. 10⁵ dyne
B. 10⁶ dyne
C. 10⁷ dyne
D. 10⁸ dyne
Answer : A

38. One half of a vibration of a body, is called
A. Period time
B. Oscillation
C. Beat
D. Amplitude
Answer : C

39. 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

40. The acceleration of a train starting from rest at any instant is 1/6(V + 1) m/sec² where V is the velocity of the train in m/sec. The train will attain a velocity of 36 km/hour after travelling a distance of
A. 2000 m
B. 2100 m
C. 2200 m
D. 2300 m
Answer : D

41. 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

42. The practical units of work, is
A. Erg
B. Joule
C. Newton
D. Dyne
Answer : B

43. 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

44. 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

45. 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

46. A ball moving with a velocity of 5 m/sec impinges a fixed plane at an angle of 45° and its direction after impact is equally inclined to the line of impact. If the coefficient of restitution is 0.5, the velocity of the ball after impact will be
A. 0.5 m/sec
B. 1.5 m/sec
C. 2.5 m/sec
D. 3.5 m/sec
Answer : C

47. 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

48. If two forces are in equilibrium, then the forces must (i) Be equal in magnitude (ii) Be opposite in sense (iii) Act along the same line The correct answer is
A. (i) and (ii)
B. (i) and (iii)
C. Only (i)
D. All (i), (ii) and (iii)
Answer : D

49. A marble ball is rolled on a smooth floor of a room to hit a wall. If the time taken by the ball in returning to the point of projection is twice the time taken in reaching the wall, the coefficient of restitution between the ball and the wall, is
A. 0.25
B. 0.50
C. 0.75
D. 1.0
Answer : B

50. Effect of a force on a body depends upon its
A. Direction
B. Magnitude
C. Position
D. All the above
Answer : D