Applied Mechanics and Graphic Statics MCQ Solved Paper for CAT

1. Minimum pull in a suspended cable with supports at two ends is equal to
A. Horizontal thrust
B. Support reactions
C. Resultant of horizontal thrust and support reaction
D. Half the weight of the cable
Answer : A

2. 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

3. Which of the following is a scalar quantity?
A. Energy
B. Momentum
C. Torque
D. Impulse
Answer : A

4. 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

5. ? 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. ?
B. 2?
C. 3?
D. ½?
Answer : B

6. 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
Answer : D

7. 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

8. The reaction at the support D of the continuous beam ABCD, hinged at two points shown in below figure is
A. 1.6 t ?
B. 1.6 t ?
C. 0.5 t ?
D. 0.5 t ?
Answer : B

9. If a body is acted upon by a number of coplanar non-concurrent forces, it may
A. Rotate about itself without moving
B. Move in any one direction
C. Move in any one direction rotating about itself
D. All the above
Answer : D

10. The frequency of oscillation on moon as compared to that on earth, will be
A. 2.44 times more
B. 2.44 times less
C. 3 times less
D. 3 times more
Answer : B

11. A cable loaded with 0.5 tonne per horizontal metre span is stretched between supports in the same horizontal line 400 m apart. If central dip is 20 m, the minimum tension in the cable, will be
A. 200 tonnes at the centre
B. 500 tonnes at the centre
C. 200 tonnes at the right support
D. 200 tonnes at the left support
Answer : B

12. 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. 11,000 km per hour
Answer : @

13. 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

14. 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

15. To attain the synchronous orbit, the launch of a satellite, is done from a place
A. On equator
B. On 30° latitude
C. On 45° latitude
D. On the poles
Answer : A

16. 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
Answer : B

17. The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be
A. sin (? + ?)/sin (? - ?)
B. sin (? - ?)/sin (? + ?)
C. cos (? - ?)/cos (? + ?)
D. tan (? - ?)/tan (? + ?)
Answer : B

18. 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

19. 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
Answer : B

21. One Newton is equivalent to
A. 10⁵ dyne
B. 10⁶ dyne
C. 10⁷ dyne
D. 10⁸ dyne
Answer : A

22. 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

23. Newtons Law of Motion is:
A. Everybody 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
Answer : D

24. 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

25. 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
Answer : A

26. The diagram showing the point of application and line of action of forces in their plane is called
A. Vector diagram
B. Space diagram
C. Force diagram
D. Funicular diagram
Answer : B

27. When a body slides down an inclined surface, the acceleration (f) of the body, is given by
A. f = g
B. f = g sin ?
C. f = g cos ?
D. f = g tan ?
Answer : B

28. A shell of mass 100 kg travelling with a velocity of 10 m/sec 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

29. A glass ball is shot to hit a wall from a point on a smooth floor. If the ball returns back to the point of projection in twice the time taken in reaching the wall, the coefficient of restitution between the glass ball and the wall is
A. 0.25
B. 0.33
C. 0.40
D. 0.50
Answer : D

30. Angular acceleration of a particle may be expressed as
A. Radians/sec²
B. Degrees/sec²
C. Revolutions/sec
D. All the above
Answer : D

31. The bending moment in an arch is proportional to
A. Vertical ordinate of funicular polygon
B. Vertical ordinate of the arch
C. Intercept between the arch axis and the funicular polygon
D. None of these
Answer : C

32. 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
Answer : A

33. 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)
Answer : C

34. 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

35. The rotational velocity of a satellite is increased by 450 m per second if its launch is done from equator
A. Eastward
B. Northward
C. Westward
D. Southward
Answer : A

36. Which one of the following statements is true?
A. The tangent of the angle of friction is equal to coefficient of friction
B. The angle of repose is equal to angle of friction
C. The tangent of the angle of repose is equal to coefficient of friction
D. All the above
Answer : D

37. Moment of inertia of a squares of side b about an axis through its centre of gravity, is
A. b³/4
B. b⁴/12
C. b⁴/3
D. b⁴/8
Answer : B

38. 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. ? = ?/4 - ?/2
B. ? = ?/2 + ?/2
C. ? = ?/2 - ?/2
D. ? = ?/4 - ?/2
Answer : B

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

41. Energy may be defined as
A. Power of doing work
B. Capacity of doing work
C. Rate of doing work
D. All the above
Answer : B

42. 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

43. Which of the following represents the state of neutral equilibrium?
A. A cube resting on one edge
B. A smooth cylinder lying on a curved surface
C. A smooth cylinder lying on a convex surface
D. None of the above
Answer : D

44. For a body moving with simple harmonic motion, the number of cycles per second, is known as its
A. Oscillation
B. Amplitude
C. Periodic time
D. Frequency
Answer : D

45. 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

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

47. 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. T = g(M₁ - M₂)/(M₁ + M₂)
B. T = g(M₁ + M₂)/(M₁ × M₂)
C. T = g(M₂ - M₁)/(M₁ + M₂)
D. T = g(M₂ + M₁)/(M₂ - M₁)
Answer : A

48. The ratio of the reactions R_A and R_B of a simply supported beam shown in below figure is
A. 0.50
B. 0.40
C. 0.67
D. 1.00
Answer : D

49. 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. None of these
Answer : C

50. The resolved part of the resultant of two forces inclined at an angle ? in a given direction is
A. Algebraic sum of the resolved parts of the forces in the direction
B. Arithmetical sum of the resolved parts of the forces in the direction
C. Difference of the forces multiplied by cosine ?°
D. Sum of the forces multiplied by the tangent ?°
Answer : A