### Civil Engineering - Applied Mechanics MCQs Part 3

1. If two bodies of masses M1 and M2(M1 > M2) are connected by alight inextensible string passing over a smooth pulley, the tension in the string, will be given by

A.
B.
C.
D.

2. For a simple pendulum, the period of one oscillation is

A.
2πl/2g
B.
2π2g/l
C.
2πl/g
D.
2πg/2l.

3. A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The velocity ratio of the lifting machine is

A.
50
B.
55
C.
60
D.
65
E.
70.

4. 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 raction and limiting friction
D.
The force of friction at which the body is just about to move.

5. The resultant of two forces acting at right angles is 5 kgf and if they act at an angle of 60°, it is 37 kgf. The magnitudes of the forces are :

A.
2 kgf, 3 kgf
B.
3 kgf, 4 kgf
C.
4 kgf, 5 kgf
D.
5 kgf, 3 kgf.

6. A body A of mass 6.6 kg which is lying on a horizontal platform 4.5 m from its edge is connected to the end of a light string whose other end is supporting a body of mass 3.2 kg as shown in below figure. If the friction between the platform and the body A is 1/3, the acceleration is

A. 0.5 m/sec2
B. 0.75 m/sec2
C. 1.00 m/sec2
D. 1.25 m/sec2.

7. 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
E. none of these.

8. 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.

9. A square hole is made in a circular lamina, the diagonal of the square is equal to the radius of the circleas shown in below figure the shift in the centre of gravity is

A.
B.
C.
D.

10. For perfectly elastic bodies, the value of coefficient of restitution is

A. zero
B. 0.5
C. 1.0
D. between 0 and 1.

11. Time of flight of a projectile on a horizontal plane, is

A.
B.
C.
D.

12. 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.

13. The acceleration of a train starting from rest at any instant is 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
E. 2500 m.

14. The maximum frictional force which comes into play, when a body just begins to slide over the surface of a an other body, is known

A. sliding friction
B. rolling friction
C. limiting friction
D. none of these.

15. If G is the Gauge of track, v is velocity of the moving vehicle, g is the acceleration due to gravity and r is the radius of a circular path, the required superelevation is

A.
B.
C.
D.

16. If v and ω are linear and angular velocities, the centripetal acceleration of a moving body along the circular path of radius r, will be

A.
B.
C.
D.
E. rω.

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

A. 7 kg
B. 1 kg
C. 5 kg
D. 1/7 kg
E. none of these.

18. The c.g. of the shaded area of the below figure from the x-axis is

A.
B.
C.
D.
E.

19. 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.

20. 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

A. α = -
B. α = +
C. α = -
D. α = -
E. α = -

21. A stone of mass 1 kg is tied to a string of length 1 m and whirled in a horizontal circle at a constant angular speed 5 rad/sec. The tension in the string is,

A. 5 N
B. 10 N
C. 15 N
D. 25 N
E. None of these.

22. For a simple pendulum, time period for a beat, is

A. πl/g
B. π2l/g
C. πg/2l
D. πl/2g
E. π2g/l.

23. 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.

24. The apparent weight of a man in a moving lift is less than his real weight when it is going down with

A. uniform speed
B. an acceleration
C. linear momentum
D. retardation.

25. P is the force acting on a body whose mass is m and acceleration is f. The equation P - mf = 0, is known as

A. equation of dynamics
B. equation of dynamic equilibrium
C. equation of statics
D. none of these.

26. Newtons's Law of Motion is :

A. Every body continues in its state of rest or of uniform motion, in a straight line, unless it is acted upon by some external force
B. The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts
C. To every action, there is always an equal and opposite reaction
D. All the above.

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

A. ED
B. DC
C. BC
D. BD.

28. The equation of motion of a particle starting from rest along a straight line is x = t3 - 3l2 + 5. The ratio of the velocities after 5 sec and 3 sec will be

A. 2
B. 3
C. 4
D. 5
E. 4.5

29. 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
E. 37.5 cm4.

30. The height at which the end of a rope of length l should be tied so that a man pulling at the other end may have the greatest tendency to overturn the pillar, is

A. l
B.
C.
D.
E. none of these.

31. The resultant of two forces acting at right angles is 34 kg and acting at 60° is 70 kg. The forces are

A. 1 kg and 4 kg
B. 2 kg and 3 kg
C. 3 kg and 5 kg
D. 3 kg and 5 kg
E. 3 kg and 5 kg.

32. The velocity of a body fallen from height h, on reaching the ground is given by

A. v = 2gh
B. v = 2gh2
C. v = 2gh
D. v = 1/2gh
E. h2/2g

33. 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.

34. μ 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. μ
B. 2μ
C. 3μ
D. μ.

35. 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).

36. 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.

37. 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
E. none of these.

38. 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

A. 0.33
B. 0.44
C. 0.57
D. 0.67

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

A.
B.
C.
D.

40. 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

41. 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

42. 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
E. none of these.

43. The moment of inertia of the shaded portion of the area shown in below figure about the X-axis, is

A. 229.34 cm4
B. 329.34 cm4
C. 429.34 cm4
D. 529.34 cm4.

44. 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.

45. A satellite is said to move in a synchronous orbit if it moves at an altitude of 36, 000 km with a maximum velocity of about

A. 7000 km per hour
B. 8000 km per hour
C. 9000 km per hour
D. 10, 000 per hour
E. 11, 000 km per hour.

46. Pick up the incorrect statement from the following :

A. The C.G. of a circle is at its centre
B. The C.G. of a triangle is at the intersecton of its medians
C. The C.G. of a rectangle is at the intersection of its diagonals
D. The C.G. of a semicircle is at a distance of r/2 from the centre
E. The C.G. of an ecllipse is at the intersection of axes.

47. A 49 kg lady stands on a spring scale in an elevator. During the first 5 sec, starting from rest, the scale reads 69 kg. The velocity of the elevator will be

A. 10 m/sec
B. 15 m/sec
C. 20 m/sec
D. 25 m/sec.

48. 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

A. rubber and lead balls undergo equal changes in momentum
B. change in momentum suffered by lead ball is less that of rubber ball
C. momentum of rubber ball is less than that of lead ball
D. none of these.

49. 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°

50. 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
E. 3.0 m/sec