About Applied Mechanics

Following are some of the multiple choice questions on the Applied Mechanics with answers that will help the students in developing their knowledge.

Applied Mechanics MCQ

1. 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

  • 0.25 cm
  • 0.50 cm
  • 0.75 cm
  • 1.00 cm

2. The following is not a law of static friction:

  • The force of friction always acts in a direction opposite to that in which the body tends to move
  • The force of friction is dependent upon the area of contact
  • The force of friction depends upon the roughness of the surface
  • The magnitude of the limiting friction bears a constant ratio to the normal reaction between two surfaces

3. M.I. of solid sphere, is

  • ⅔ Mr²
  • ½ Mr²
  • Mr²
  • πr4/2

4. Two forces act an angle of 120°. If the greater force is 50 kg and their resultant is perpendicular to the smaller force, the smaller force is

  • 20 kg
  • 25 kg
  • 30 kg
  • 35 kg

5. The motion of a particle is described by the relation x = t²- 10t + 30, where x is in meters and t in seconds. The total distance travelled by the particle from t = 0 to t = 10 seconds would be

  • Zero
  • 30 m
  • 50 m
  • 60 m

6. When a circular wheel rolls on a straight track, then the shape of body centrode and space centrode respectively are

  • Straight line and parabola
  • Straight line and circle
  • Circle and straight line
  • Circle and parabola

7. A cable loaded with 10 kN/m of span is stretched between supports in the same horizontal line 100 m apart. If the central dip is 10 m, then the maximum and minimum pull in the cable respectively are

  • 1346.3 kN and 1500 kN
  • 1436.2 kN and 1250 kN
  • 1346.3 kN and 1250 kN
  • 1436.2 kN and 1500 kN

8. Time period and length of a second’s pendulum respectively are

  • 1 sec and 99.4 cm
  • 1 sec and 92.7 cm
  • 2 sec and 99.4 cm
  • 2 sec and 92.7 cm

9. The angles between two forces to make their resultant a minimum and a maximum respectively are

  • 0° and 90°
  • 180° and 90°
  • 90° and 180°
  • 180° and 0°

10. 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

  • 2 J
  • 4 J
  • 6 J
  • 8 J

11. A sphere is resting on two planes BA and BC which are inclined at 45° and 60° respectively with the horizontal. The reaction on the plane BA will be

  • Less than that on BC
  • More than that of BC
  • Equal to that on BC
  • None of these

12. In a simple screw jack, the pitch of the screw is 9 mm and length of the handle operating the screw is 45 cm. The velocity ratio of the system is

  • 1.5
  • 5
  • 25
  • 314

13. If ‘α’ is the angular acceleration of a compound pendulum whose angular displacement is ‘θ’, the frequency of the motion is

  • 2π √(α/θ)
  • (1/2π) √(α/θ)
  • 4π √(α/θ)
  • 2π √(α - θ)

14. For the given values of initial velocity of projection and angle of inclination of the plane, the maximum range for a projectile projected upwards will be obtained, if the angle of projection is

  • α = π/4 - β/2
  • α = π/2 + β/2
  • α = β/2 - π/2
  • α = π/4 - β/2

15. For a given velocity of a projectile, the range is maximum when the angle of projection is

  • 30°
  • 45°
  • 90°

16. On a ladder resisting on a smooth ground and leaning against a rough vertical wall, the force of friction acts

  • Towards the wall at its upper end
  • Away from the wall at its upper end
  • Upwards at its upper end
  • Downwards at its upper end

17. On a ladder resting on a rough ground and leaning against a smooth vertical wall, the force of friction acts

  • Downwards at its upper end
  • Upwards at its upper end
  • Perpendicular to the wall at its upper end
  • Zero at its upper end

18. One Newton force, is

  • 10³ dynes
  • 10⁴ dynes
  • 10⁵ dynes
  • 10⁶ dynes

19. 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

  • gra/h
  • √(gra/h)
  • ∛(gra/h)
  • 4√(gra/h)

20. 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

  • Original velocity in the same direction
  • Half the original velocity in the same direction
  • Half the original velocity in the opposite direction
  • Original velocity in the opposite direction

21. If two forces of 3 kg and 4 kg act at right angles to each other, their resultant force will be equal to

  • 7 kg
  • 1 kg
  • 5 kg
  • None of these

22. 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

  • Rubber and lead balls undergo equal changes in momentum
  • Change in momentum suffered by lead ball is less that of rubber ball
  • Momentum of rubber ball is less than that of lead ball
  • None of these

23. The centre of gravity of a trapezoidal dam section whose top width is a, bottom width is band the vertical side is a, from its vertical face is

  • (a² + ab + b²)/3 (a + b)
  • (b² + bc + c²)/3 (b + c)
  • (a² + ab + c²)/3 (a + c)
  • None of these

24. If the linear velocity of a point on the rim of a wheel of 10 m diameter, is 50 m/sec, its angular velocity will be

  • 20 rad/sec
  • 15 rad/sec
  • 10 rad/sec
  • 5 rad/sec

25. A body of weight ‘w’ placed on an inclined plane is acted upon by a force ‘P’ parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is ‘θ’ and angle of friction is ‘φ’, the minimum value of ‘P’, is

  • w sin (φ - θ)/cos φ
  • w sin (θ - φ)/cos φ
  • w cos (θ + φ)/cos φ
  • w sinθ cos(θ - φ)/sin φ

26. 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:

  • 40 g
  • 60 g
  • 80 g
  • 100 g

27. The unit of force in C.G.S. system of units, is called

  • Dyne
  • Newton
  • Kg
  • All the above

28. The unit of moments in M.K.S system, is

  • kg.m
  • kg/m2
  • kg/sec2
  • kg/sec

29. A stone is thrown vertically upwards with a vertical velocity of 49 m/sec. It returns to the ground in

  • 5 sec
  • 8 sec
  • 10 sec
  • 20 sec

30. If a particle moves with a uniform angular velocity ‘ω’ radians/sec along the circumference of a circle of radius ‘r’, the equation for the velocity of the particle, is

  • v = ω √(y² - r²)
  • y = ω √(y - r)
  • v = ω √(r² + y²)
  • v = ω √(r² - y²)

31. Periodic time of a particle moving with simple harmonic motion is the time taken by the particle for

  • Half oscillation
  • Quarter oscillation
  • Complete oscillation
  • None of these

32. Two objects moving with uniform speeds are 5 m apart after 1 second when they move towards each other and are 1 m apart when they move in the same direction.The speeds of the objects are:

  • 2 m/sec and 2 m/sec
  • 3 m/sec and 2 m/sec
  • 3 m/sec and 3 m/sec
  • 4 m/sec and 6 m/sec

33. A bullet weighing 200 g is fired horizontally with a velocity of 25 m/sec from a gun carried on a carriage which together with the gun weighs 100 kg. The velocity of recoil of the gun, will be

  • 0.01 m/sec
  • 0.05 m/sec
  • 1.00 m/sec
  • 1.5 m/see

34. A satellite goes on moving along its orbit round the earth due to

  • Gravitational force
  • Centrifugal force
  • Centripetal force
  • None of these

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

  • Gravitational force
  • Centripetal force
  • Centrifugal force
  • None of these

36. In SI units, the units of force and energy are respectively

  • Newton and watt
  • Dyne and erg
  • Newton and joule
  • kg wt and joule

37. The dimensions of Gravitational Universal constant ‘G’ are

  • M-1L2r2
  • M-1L3r2
  • M-2L3T2
  • M1L3T2

38. The motion of a bicycle wheel is

  • Translatory
  • Rotary
  • Rotary and translatory
  • Curvilinear

39. The member which does not carry zero force in the structure shown in below figure, is

  • ED
  • DC
  • BC
  • BD

40. The vertical reaction at the support ‘A’ of the structure shown in below figure, is

  • 1 t
  • 2 t
  • 3 t
  • 3.5 t

41. 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

  • g1
  • g2
  • g1/g2
  • g2/g1

42. If the angular distance, 0 = 2t³ ‑ 3t², the angular acceleration at t = 1 sec. is

  • 1 rad/sec²
  • 4 rad/sec²
  • 6 rad/sec²
  • 12 rad/sec²

43. The centre of gravity of a quadrant of a circle lies along its central radius at a distance of

  • 0.2 R
  • 0.4 R
  • 0.3 R
  • 0.6 R

44. The centre of gravity of the trapezium as shown in below figure from the side is at a distance of

  • (h/3) × [(b + 2a)/(b + a)]
  • (h/3) × [(2b + a)/(b + a)]
  • (h/2) × [(b + 2a)/(b + a)]
  • (h/2) × [(2b + a)/(b + a)]

45. Effect of a force on a body depends upon its

  • Direction
  • Magnitude
  • Position
  • All the above

46. In a lifting machine a weight of 5 kN is lifted through 200 mm by an effort of 0.1 kN moving through 15 m. The mechanical advantage and velocity ratio of the machine are respectively

  • 50 and 75
  • 75 and 50
  • 75 and 75
  • 50 and 50

47. 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

  • 0.25
  • 0.50
  • 0.75
  • 1.0

48. A ball is dropped from a height of 2.25 m on a smooth floor and rises to a height of 1.00 m after the bounce. The coefficient of restitution between the ball and the floor is

  • 0.33
  • 0.44
  • 0.57
  • 0.67

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

  • Its longer side
  • Its shorter side
  • The diagonal of the parallelogram which does not pass through the point of intersection of the forces
  • The diagonal of the parallelogram which passes through the point of intersection of the forces

50. The resultant of two forces ‘P’ and ‘Q’ acting at an angle ‘θ’, is

  • P² + Q² + 2P sin θ
  • P² + Q² + 2PQ cos θ
  • P² + Q² + 2PQ tan θ
  • √(P² + Q² + 2PQ cos θ)

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