Applied Mechanics and Graphic Statics MCQ Solved Paper for RRB NTPC

1. The inherent property of a body which offers reluctance to change its state of rest or uniform motion, is
A. Weight
B. Mass
C. Inertia
D. Momentum
Answer : C

2. 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

3. 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

4. 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

5. The vertical reaction at the support A of the structure shown in below figure, is
A. 1 t
B. 2 t
C. 3 t
D. 3.5 t
Answer : C

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

7. Two circular discs of same weight and thickness are made from metals having different densities. Which disc will have the larger rotational inertia about its central axis?
A. Disc with larger density
B. Disc with smaller density
C. Both discs will have same rotational inertia
D. None of the above
Answer : B

8. A shell travelling with a horizontal velocity of 100 m/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan1 x, where x is
A. 3/4
B. 4/5
C. 5/3
D. 3/5
Answer : D

9. A weight W is suspended at the free end of a light member hinged to a vertical wall. If the angle of inclination of the member with the upper wall is ?°, the force introduced in the member, is
A. W sec ?
B. W cos ?
C. W sin ?
D. W cosec ?
Answer : A

10. Force polygon method is applicable for
A. Any coplanar force system
B. A system of parallel forces only
C. Concurrent coplanar force system
D. Non-concurrent coplanar force system
Answer : C

11. 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

12. 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

13. The ends of a string weighing w/metre are attached to two points at the same horizontal level. If the central dip is very small, the horizontal tension of the string throughout is
A. wl/4d
B. wl²/4d
C. wl²/8d
D. wl²/16d
Answer : C

14. The angular speed of a car while taking a circular turn of radius 100 m at 36 km/hour, is
A. 0.1 radian/sec
B. 1 radian/sec
C. 100 radian/sec
D. 1000 radian/sec
Answer : A

15. If a body is lying on a plane whose inclination with the horizontal is less than the angle of friction, then? (i) A force is required to move the body upwards (ii) A force is required to move the body downward (iii) The body will not be in equilibrium The correct answer is
A. Only (i)
B. Only (ii)
C. Both (i) and (ii)
D. Both (i) and (iii)
Answer : C

16. A spring scale in a stationary lift shows a reading of 60 kg for a man standing on it. If the lift starts descending at an acceleration of g/5, the scale reading would be
A. 48 kg
B. 60 kg
C. 72 kg
D. None of these
Answer : A

17. If the velocity of projection is 4 m/sec and the angle of projection is ?°, the maximum height of the projectile from a horizontal plane, is
A. u² cos² ?/2g
B. u² sin² ?/2g
C. u² tan² ?/2g
D. u² sin 2?/2g
Answer : B

18. A disc of mass 4 kg, radius 0.5 m and moment of inertia 3 kgm² rolls on a horizontal surface so that its center moves with speed 5 m/see. Kinetic energy of the disc is
A. 50 J
B. 150 J
C. 200 J
D. 400 J
Answer : C

19. A satellite goes on moving along its orbit round the earth due to
A. Gravtational force
B. Centrifugal force
C. Centripetal force
D. None of these
Answer : B

20. Williot-Mohr diagram is used to determine deflection in
A. Trusses only
B. Beam only
C. Rigid frames only
D. Any type of structure
Answer : A

21. 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

22. If g1 and g2 are the gravitational accelerations on two mountains A and B respectively, the weight of a body when transported from A to B will be multiplied by
A. g1
B. g2
C. g1/g2
D. g2/g1
Answer : D

23. A particle is dropped from a height of 3 m on a horizontal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the ball will rebound after striking the floor is
A. 0.5 m
B. 0.75 m
C. 1.0 m
D. 1.5 m
Answer : B

24. The instantaneous centre of a member lies at the point of intersection of two lines drawn at the ends of the member such that the lines are inclined to the direction of motion of the ends at
A. 30°
B. 45°
C. 60°
D. 90°
Answer : D

25. 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

26. Power developed by a torque, is
A. 2?NT kg m/min
B. 2?NT/4500 h.p
C. 2?NT /60 watts
D. All the above
Answer : D

27. A trolley wire weighs 1 kg per metre length. The ends of the wire are attached to two poles 20 m apart. If the horizontal tension is 1000 kg, the central dip of the cable is
A. 2 cm
B. 3 cm
C. 4 cm
D. 5 cm
Answer : D

28. A ball of mass 250 g moving on a smooth horizontal table with a velocity of 10 m/sec hits an identical stationary ball B on the table. If the impact is perfectly plastic, the velocity of the ball B just after impact would be
A. Zero
B. 5 m/sec
C. 10 m/sec
D. None of these
Answer : A

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. The time period of a simple pendulum depends on (i) Mass of suspended particle (ii) Length of the pendulum (iii) Acceleration due to gravity The correct answer is
A. Only (i)
B. Both (ii) and (iii)
C. Both (i) and (iii)
D. All are correct
Answer : B

31. 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

32. Pick up the correct statement from the following:
A. Nature plays an important role in the launch of a satellite
B. The earth's gravity reduces the speed of a satellite by 32 km per second
C. The gravitational force relents as the satellite climbs higher
D. All the above
Answer : D

33. The motion of a bicycle wheel is
A. Translatory
B. Rotary
C. Rotary and translatory
D. Curvilinear
Answer : C

34. The ratio of the speed of a rolling cylinder to the speed of sliding cylinder is
A. Less than 1
B. Equal to 1
C. Between 1 and 2
D. Greater than 2
Answer : A

35. If a particle is projected inside a horizontal tunnel which is 554 cm high with a velocity of 60 m per sec, the angle of projection for maximum range, is
A. 8°
B. 9°
C. 10°
D. 11°
Answer : C

36. 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

37. 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

38. Select the correct statement
A. The body centrode rolls on the space centrode
B. The space centrode rolls on the body centrode
C. Both body and space centrodes may role on each other
D. The body centrode never touches space centrode
Answer : A

39. A shell of mass 100 kg travelling with a velocity of 10 m/se breaks into two equal pieces during an explosion which provides an extra kinetic energy of 20000 Joules. If the pieces continue to move in the same direction as before, then the speed of the faster one must be
A. 20 m/sec
B. 30 m/sec
C. 40 m/sec
D. 50 m/sec
Answer : B

40. If a spherical body is symmetrical about its perpendicular axes, the moment of inertia of the body about an axis passing through its centre of gravity as given by Routh's rule is obtained by dividing the product of the mass and the sum of the squares of two semi-axes by n. Where, n is
A. 2
B. 3
C. 4
D. 5
Answer : D

41. 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

42. 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

43. 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

44. 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 : @

45. For lifting a load of 50 kg through a distance of 2.5 cm, an effort of 12.5 kg is moved through a distance of 40 cm. The efficiency of the lifting machine, is
A. 60 %
B. 65 %
C. 70 %
D. 75 %
Answer : D

46. Coefficient of friction depends on
A. Nature of surfaces only
B. Area of contact only
C. Both (A) and (B)
D. None of the above
Answer : A

47. If the resultant of two forces P and Q acting at an angle ? makes an angle ? with P, then tan ? equals
A. P sin ?/P - Q cos ?
B. Q sin ?/P + Q cos ?
C. P sin ?/P + Q tan ?
D. Q sin ?/P + Q sin ?
Answer : B

48. 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

49. 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

50. 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