Applied Mechanics and Graphic Statics MCQ Solved Paper for SSC CPO

1. The characteristic of a couple is:
A. Algebraic sum of forces, constituting a couple is zero
B. Algebraic sum of moments of forces, constituting a couple, about any point, is same
C. A couple can be never the balanced by a single force
D. All the above
Answer : D

2. 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
A. 20 rad/sec
B. 15 rad/sec
C. 10 rad/sec
D. 5 rad/sec
Answer : D

3. 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

4. Rate of change of angular momentum is equal to
A. Force
B. Torque
C. Linear momentum
D. Impulse
Answer : B

5. If l is the span of a light suspension bridge whos 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
Answer : B

6. The condition of equilibrium for any system of forces in a plane is
A. That polygon of forces must close
B. That resultant couple must be zero
C. Both (A) and (B)
D. None of the above
Answer : C

7. 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 : @

8. 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

9. The units of inertia of mass are
A. kg/m
B. kg/m²
C. m⁴
D. kg-m²
Answer : D

10. 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
A. Original velocity in the same direction
B. Half the original velocity in the same direction
C. Half the original velocity in the opposite direction
D. Original velocity in the opposite direction
Answer : D

11. Ball A of mass 250 g moving on a smooth horizontal table with a velocity of 10 m/s hits an identical stationary ball B on the table. If the impact is perfectly elastic, 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 : C

12. The motion of a bicycle wheel is
A. Translatory
B. Rotary
C. Rotary and translatory
D. Curvilinear
Answer : C

13. 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

14. 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

15. 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

16. 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

17. If the horizontal range is 2.5 times the greatest height, the angle of projection of the projectile, is
A. 57°
B. 58°
C. 59°
D. 60°
Answer : B

18. A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about (Assume g = 10 m/sec²)
A. 1/4
B. 1/3
C. 1/2
D. 1/5
Answer : A

19. On a ladder resisting on a smooth ground and leaning against a rough vertical wall, the force of friction acts
A. Towards the wall at its upper end
B. Away from the wall at its upper end
C. Upwards at its upper end
D. Downwards at its upper end
Answer : C

20. Joule is the unit of
A. Power
B. Impuls
C. Work
D. Momentum
Answer : C

21. A simple pendulum of length l has an energy E, when its amplitude is A. If the length of pendulum is doubled, the energy will be
A. E
B. E/2
C. 2E
D. 4E
Answer : B

22. The rate of change of displacement of a body with respect to its surrounding, is known
A. Velocity
B. Acceleration
C. Speed
D. None of these
Answer : C

23. 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
A. Less than that on BC
B. More than that of BC
C. Equal to that on BC
D. None of these
Answer : B

24. 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

25. 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

26. The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then,
A. P = R
B. Q = R
C. P = Q
D. None of the above is correct
Answer : B

27. 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

28. A geo-stationary satellite is one which orbits the earth with a velocity of rotation of
A. Moon
B. Earth
C. Sun
D. Pole
Answer : B

29. The length of a Second's pendulum, is
A. 99.0 cm
B. 99.4 cm
C. 100 cm
D. 101 cm
Answer : B

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

31. 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

32. If two forces acting at a point are in equilibrium, they must be equal in magnitude and their line of action must be along
A. The same line in the same sense
B. The same line in opposite sense
C. The perpendicular to both the lines
D. None of these
Answer : B

33. The angle which an inclined surface makes with the horizontal when a body placed on it is on the point of moving down, is called
A. Angle of repose
B. Angle of friction
C. Angle of inclination
D. None of these
Answer : A

34. A spring scale in a stationary lift shows a reading of 60 kg for a man standing on it. If the lift starts descending at an acceleration of g/5, the scale reading would be
A. 48 kg
B. 60 kg
C. 72 kg
D. None of these
Answer : A

35. 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
Answer : A

36. If the radius of the earth is 600 km the height of a mountain above sea level at the top of which a beat seconds pendulum at sea level, looses 27 seconds a day, is
A. 500 metres
B. 1000 metres
C. 1500 metres
D. 2000 metres
Answer : D

37. If a projectile is fired with an initial velocity of 10 m/sec at an angle of 60° to the horizontal, its horizontal and vertical velocity at the highest point of trajectory are
A. 0 and 5 m/sec
B. 5 m/sec and 0
C. 5?3 m/sec and 0
D. 5 and 5?3 m/sec
Answer : B

38. 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

39. 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

40. A particle moves with a velocity of 2 m/sec in a straight line with a negative acceleration of 0.1 m/sec2. Time required to traverse a distance of 1.5 m, is
A. 40 sec
B. 30 sec
C. 20 sec
D. 15 sec
Answer : C

41. 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
Answer : D

42. A particle moving with a simple harmonic motion, attains its maximum velocity when it passes
A. The extreme point of the oscillation
B. Through the man position
C. Through a point at half amplitude
D. None of these
Answer : B

43. The following factor affects the orbit of a satellite up to an altitude of 720 km from the earth's surface
A. Uneven distribution of the gravitational field
B. Gravity of the sun and the moon
C. Aerodynamic forces
D. None of these
Answer : D

44. If A is the amplitude of particle executing simple harmonic motion, then the total energy E of the particle is
A. Proportional to A
B. Proportional to A²
C. Proportional to 1/A²
D. Independent of A
Answer : B

45. For a given velocity of a projectile, the range is maximum when the angle of projection is
A. 30°
B. 45°
C. 90°
D. 0°
Answer : B

46. 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

47. The centre of gravity of a quadrant of a circle lies along its central radius at a distance of
A. 0.2 R
B. 0.4 R
C. 0.3 R
D. 0.6 R
Answer : D

48. 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

49. 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

50. In 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