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

1. For a non-concurrent force system to be in equilibrium
A. Only the closure of force polygon is sufficient
B. Only the closure of funicular polygon is sufficient
C. Both force polygon and funicular polygon must close
D. None of the above
Answer : C

2. When a body in equilibrium undergoes an infinitely small displacement, work imagined to be done, is known as
A. Imaginary work
B. Negative work
C. Virtual work
D. None of these
Answer : C

3. 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

4. In a lifting machine with efficiency 60%, an effort of 200 N is required to raise a load of 6 kN. The velocity ratio of the machine is
A. 30
B. 50
C. 60
D. 80
Answer : B

5. The force which produces an acceleration of 1 m/sec2 in a mass of one kg, is called
A. Dyne
B. Newton
C. Joule
D. Erg
Answer : B

6. M.I. of solid sphere, is
A. ? Mr²
B. ½ Mr²
C. Mr²
D. ?r⁴/2
Answer : C

7. The resultant of two forces P and Q acting at an angle ?, is
A. P² + Q² + 2P sin ?
B. P² + Q² + 2PQ cos ?
C. P² + Q² + 2PQ tan ?
D. ?(P² + Q² + 2PQ cos ?)
Answer : D

8. Periodic time of body moving with simple harmonic motion, is
A. Directly proportional to its angular velocity
B. Directly proportional to the square of its angular velocity
C. Inversely proportional to the square of its angular velocity
D. Inversely proportional to its angular velocity
Answer : D

9. 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

10. 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

11. The beam shown in below figure is supported by a hinge at A and a roller at B. The reaction RA of the hinged support A of the beam, is
A. 10.8 t
B. 10.6 t
C. 10.4 t
D. 10.2 t
Answer : D

12. 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

13. 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

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

15. The angle of friction is:
A. The ratio of the friction and the normal reaction
B. The force of friction when the body is in motion
C. The angle between the normal reaction and the resultant of normal reaction and limiting friction
D. The force of friction at which the body is just about to move
Answer : C

16. Principle of Transmissibility of Forces states that, when a force acts upon a body, its effect is
A. Maximum if it acts at the centre of gravity of the body
B. Different at different points on its line of
C. Same at every point on its line of action
D. Minimum if it acts at the C.G. of the body
Answer : C

17. The horizontal reaction at the support A of the structure shown in below figure, is

A. Zero
B. 2 t
C. 3 t
D. 1 t
Answer : A

18. If the tension in a cable supporting a lift moving upwards is twice the tension when the lift is moving downwards, the acceleration of the lift, is
A. g/2
B. g/3
C. g/4
D. g/5
Answer : B

19. The unit of rotational inertia of a body in C.G.S system is
A. cm⁴
B. kg.cm²
C. gm.cm²
D. gm.cm³
Answer : C

20. A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan1 x, where x is (Assume g = 10 m/sec²)
A. 3/8
B. 1/2
C. 9/5 D. 5/8
Answer : D

21. According to Law of Triangle of Forces
A. Three forces acting at a point, can be rep-resented by the sides of a triangle, each side being in proportion to the force
B. Three forces acting along the sides of a triangle are always in equilibrium
C. If three forces acting on a, point can be represented in magnitude and direction, by the sides of a triangle taken in order, these will be in equilibrium
D. If the forces acting on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant will be represented in magnitude and direction by the third side of the triangle, taken in opposite order
Answer : D

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. When two forces, each equal to P, act at 90° to each other, then the resultant will be
A. P
B. P?2
C. P/?2
D. 2P
Answer : B

29. 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

30. 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

31. 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

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 moment of inertia of a circular lamina of diameter d, about an axis perpendicular to the plane of the lamina and passing through its centre, is
A. ?d⁴/12
B. ?d⁴/16
C. ?d⁴/24
D. ?d⁴/32
Answer : D

34. 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

35. The centre of gravity of a plane lamina will not be at its geometrical centre if it is a
A. Circle
B. Equilateral triangle
C. Rectangle
D. Right angled triangle
Answer : D

36. 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

37. Time period and length of a seconds pendulum respectively are
A. 1 sec and 99.4 cm
B. 1 sec and 92.7 cm
C. 2 sec and 99.4 cm
D. 2 sec and 92.7 cm
Answer : C

38. The C.G. of a right circular cone lies on its axis of symmetry at a height of
A. h/2
B. h/3
C. h/4
D. h/5
Answer : C

39. From the circular plate of a diameter 6 cm is cut out a circular plate whose diameter is equal to radius of the plate. The C.G. of the remainder shifts from the original position through
A. 0.25 cm
B. 0.50 cm
C. 0.75 cm
D. 1.00 cm
Answer : B

40. I case of S.H.M. the period of oscillation (T), is given by
A. T = 2?/?²
B. T = 2?/?
C. T = 2/?
D. T = ?/2?
Answer : B

41. A force P of 50 N and another force Q of unknown magnitude act at 90° to each other. They are balanced by a force of 130 N. The magnitude of Q is
A. 60 N
B. 80 N
C. 100 N
D. 120 N
Answer : D

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

43. The reaction at the support A of the beam shown in below figure is
A. 2 t
B. 5.8 t
C. 0.2 t
D. 3.5 t
Answer : A

44. Time required to stop a car moving with a velocity 20 m/sec within a distance of 40 m, is
A. 2 sec
B. 3 sec
C. 4 sec
D. 5 sec
Answer : C

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

46. On a ladder resting on a rough ground and leaning against a smooth vertical wall, the force of friction acts
A. Downwards at its upper end
B. Upwards at its upper end
C. Perpendicular to the wall at its upper end
D. Zero at its upper end
Answer : D

47. 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

48. 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

49. 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

50. Joule is the unit of
A. Power
B. Impulse
C. Work
D. Momentum
Answer : C