Multiple Questions and Answers on Applied Mechanics and Graphic Statics

01. 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

02. The following is in unstable equilibrium

(A) A uniform solid cone resting on a generator on a smooth horizontal plane
(B) A uniform solid cone resting on its base on a horizontal plane
(C) A solid cube resting on one edge
(D) A satellite encircling the earth

03. 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

04. The member forces in a statically in determinate truss

(A) Can be obtained by graphic statics
(B) Cannot be obtained by graphic statics
(C) May be obtained by graphic statics
(D) Can be obtained by graphic statics by trial and error

05. 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

06. A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if

(A) Floor is smooth and wall is rough
(B) Floor is rough and wall is smooth
(C) Both floor and wall are rough
(D) Both floor and wall are smooth

07. The maximum displacement of a particle executing S.H.M. corresponds to

(A) Zero potential energy and maximum kinetic energy
(B) Zero kinetic energy and maximum potential energy
(C) Maximum kinetic energy and maximum potential energy
(D) Minimum kinetic energy and minimum potential energy

08. A sphere and a cylinder having the same mass and radii start from rest and roll down the same inclined plane. Which body gets to the bottom first?

(A) Sphere with greater rotational energy at bottom than cylinder
(B) Sphere with lesser rotational energy at bottom than cylinder
(C) Cylinder with greater rotational energy at bottom than sphere
(D) Both reach the bottom simultaneously with equal rotational energy at bottom

09. 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

10. 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

11. 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

12. Free body diagram is an

(A) Isolated joint with only body forces acting on it
(B) Isolated joint with internal forces acting on it
(C) Isolated joint with all the forces, internal as well as external, acting on it
(D) None of the above

13. The graphical method of determining the forces in the members of a truss is based on

(A) Method of joint
(B) Method of section
(C) Either method
(D) None of the two methods

14. In which of the following trusses, the method of substitution is required for determining the forces in all the members of the truss by graphic statics?

(A) Howe truss
(B) King post truss
(C) Fink truss
(D) Warren truss

15. 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

16. 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

17. 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

18. 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

19. The shape of a suspended cable under its own weight, is

(A) Parabolic
(B) Circular
(C) Catenary
(D) Elliptical

20. 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

21. Pick up the correct statement from 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

22. 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

23. 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

24. 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

25. 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

26. Three forces which act on a rigid body to keep it in equilibrium. The forces must be coplanar and

(A) Concurrent
(B) Parallel
(C) Concurrent parallel
(D) None of these

27. 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

28. The intrinsic equation of catenary is

(A) S = c tan ψ
(B) y = c cosh x/c
(C) y = c cosh ψ
(D) y = c sinh ψ

29. 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°

30. The reaction RB of the roller support B of the beam shown in below figure is (A) 10.8 t
(B) 10.6 t
(C) 10.4 t
(D) 10.2 t

31. The maximum pull in a cable, carrying a uniformly distributed load and supported at two ends which are at the same level, is at

(A) Supports
(B) Quarter span
(C) Mid span
(D) None of the above

32. A stone is whirled in a vertical circle, the tension in the string, is maximum

(A) When the string is horizontal
(B) When the stone is at the highest position
(C) When the stone is at the lowest position
(D) At all the positions

33. At a given instant ship ‘A’ is travelling at 6 km/h due east and ship ‘B’ is travelling at 8 km/h due north. The velocity of ‘B’ relative to ‘A’ is

(A) 7 km/hrs
(B) 2 km/hrs
(C) 1 km/hrs
(D) 10 km/hrs

34. The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, is

(A) 1/4
(B) 1/2
(C) 3/4
(D) 2

35. The angular speed of a car taking a circular turn of radius 100 m at 36 km/hr will be

36. 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 θ°, the force introduced in the member, is

(A) W sec θ
(B) W cos θ
(C) W sin θ
(D) W cosec θ

37. 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

38. 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

39. The force polygon representing a set of forces in equilibrium is a

(A) Triangle
(B) Open polygon
(C) Closed polygon
(D) Parallelogram

40. The centre of gravity of a homogenous body is the point at which the whole

(A) Volume of the body is assumed to be concentrated
(B) Area of the surface of the body is assumed to be concentrated
(C) Weight of the body is assumed to be concentrated
(D) All the above

41. A satellite moves in its orbit around the earth due to

(A) Gravitational force
(B) Centripetal force
(C) Centrifugal force
(D) None of these

42. The force acting on a point on the surface of a rigid body may be considered to act

(A) At the centre of gravity of the body
(B) On the periphery of the body
(C) On any point on the line of action of the force
(D) At any point on the surface normal to the line of action of the force

43. 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

44. If ‘l’ is the span of a light suspension bridge who’s each cable carries total weight (w) and the central dip is ‘y’, the horizontal pull at each support, is

(A) wl/4y
(B) wl/8y
(C) wl/2y
(D) wl

45. The C.G. of the shaded area of the below figure whose curve OM is a parabola from y-axis, is (A) a/4
(B) 3a/4
(C) 3b/10
(D) 3a/10

46. 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

47. 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

48. On a mass ‘m’ describing a circular path of radius ‘r’, the centrifugal force

(A) Acts tangentially to the circular path
(B) Acts towards the centre of rotation
(C) Acts away from the centre of rotation
(D) Is mw2r/g kgf

49. 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