Engineering Mechanics MCQ Solved Paper for SSC GD

1. Lami's theorem states that
A. Three forces acting at a point will be in equilibrium
B. Three forces acting at a point can be represented by a triangle, each side being proportional to force
C. If three forces acting upon a particle are represented in magnitude and direction by the sides of a triangle, taken in order, they will be in equilibrium
D. If three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two
Answer : D

2. One joule is equal to
A. 0.1 N-m
B. 1 N-m
C. 10 N-m
D. 100 N-m
Answer : B

3. The centre of gravity of an isosceles triangle with base (p) and sides (q) from its base is
A. [?(4p² - q²)]/6
B. (4p² - q²)/6
C. (p² - q²)/4
D. (p² + q²)/4
Answer : A

4. A redundant frame is also called __________ frame.
A. Perfect
B. Imperfect
C. Deficient
D. None of these
Answer : B

5. The forces, which meet at one point and their lines of action also lie on the same plane, are known as
A. Coplanar concurrent forces
B. Coplanar non-concurrent forces
C. Non-coplanar concurrent forces
D. Non-coplanar non-concurrent forces
Answer : A

6. The static friction
A. Bears a constant ratio to the normal reaction between the two surfaces
B. Is independent of the area of contact, between the two surfaces
C. Always acts in a direction, opposite to that in which the body tends to move
D. All of the above
Answer : D

7. Moment of inertia of a triangular section of base (b) and height (h) about an axis passing through its vertex and parallel to the base, is __________ than that passing through its C.G. and parallel to the base.
A. Nine times
B. Six times
C. Four times
D. Two times
Answer : A

8. For a self locking machine, the efficiency must be
A. Equal to 50 %
B. Less than 50 %
C. Greater than 50 %
D. 100 %
Answer : B

9. Which of the following is not the unit of power?
A. kW (kilowatt)
B. hp (horse power)
C. kcal/sec
D. kcal/kg sec
Answer : D

10. The M.I. of hollow circular section about a central axis perpendicular to section as compared to its M.I. about horizontal axis is
A. Same
B. Double
C. Half
D. Four times
Answer : B

11. The total energy possessed by a system of moving bodies
A. Is constant at every instant
B. Varies from point to point
C. Is maximum in the start and minimum at the end
D. Is minimum in the start and maximum at the end
Answer : A

12. The periodic time of one oscillation for a simple pendulum is (where l = Length of the pendulum.)
A. (1/2?). ?(l/g)
B. (1/2?). ?(g/l)
C. 2?. ?(l/g)
D. None of these
Answer : C

13. A machine having an efficiency greater than 50%, is known as
A. Reversible machine
B. Non-reversible machine
C. Neither reversible nor non-reversible machine
D. Ideal machine
Answer : A

14. The principle of transmissibility of forces states that, when a force acts upon a body, its effect is
A. Same at every point on its line of action
B. Different at different points on its line of action
C. Minimum, if it acts at the centre of gravity of the body
D. Maximum, if it acts at the centre of gravity of the body
Answer : C

15. A smooth cylinder lying on a __________ is in neutral equilibrium.
A. Curved surface
B. Convex surface
C. Horizontal surface
D. None of these
Answer : C

16. Which of the following are vector quantities?
A. Linear displacement
B. Linear velocity
C. Linear acceleration
D. All of these
Answer : D

17. In ideal machines
A. Mechanical advantage is greater than velocity ratio
B. Mechanical advantage is equal to velocity ratio
C. Mechanical advantage is less than velocity ratio
D. Mechanical advantage is unity
Answer : B

18. A differential pulley block has larger and smaller diameters of 100 mm and 80 mm respectively. Its velocity ratio is
A. 5
B. 10
C. 20
D. 40
Answer : B

19. Dynamic friction as compared to static friction is
A. Same
B. More
C. Less
D. May be less of more depending on nature of surfaces and velocity
Answer : C

20. The angle which an inclined plane makes with the horizontal when a body placed on it is about to move down is known as angle of
A. Friction
B. Limiting friction
C. Repose
D. Kinematic friction
Answer : C

21. Which of the following are vector quantities?
A. Angular displacement
B. Angular velocity
C. Angular acceleration
D. All of these
Answer : D

22. The skidding away of the vehicle on a level circular path can be avoided if the force of friction between the wheels and the ground is __________ the centrifugal force.
A. Less than
B. Greater than
C. Equal to
D. None of these
Answer : B

23. Which of the following statement is correct in connection with projectiles?
A. A path, traced by a projectile in the space, is known as trajectory.
B. The velocity, with which a projectile is projected, is known as the velocity of projection.
C. The angle, with the horizontal, at which a projectile is projected, is known as angle of projection.
D. All of the above
Answer : D

24. The coefficient of restitution for inelastic bodies is
A. Zero
B. One
C. Between zero and one
D. More than one
Answer : A

25. In a screw jack, the effort required to lift the load is given by (where W = Load lifted, ? = Helix angle, and ? = Angle of friction.)
A. P = W tan (? - ?)
B. P = W tan (? + ?)
C. P = W tan (? - ?)
D. P = W cos (? + ?)
Answer : B

26. The range of projectile will be maximum for a given velocity of projectile, when the angle of projection (?) is
A. ?/2
B. 30° + ?/2
C. 45° + ?/2
D. 60° + ?/2
Answer : C

27. Which of the following do not have identical dimensions?
A. Momentum and impulse
B. Torque and energy
C. Torque and work
D. Moment of a force and angular momentum.
Answer : D

28. The ideal angle of banking provided on the curves on roads depends upon
A. Weight of the vehicle
B. (Velocity)2 of the vehicle
C. Nature of the road surface
D. Coefficient of friction between the road and vehicle contact point
Answer : B

29. Which of the following is the locus of a point that moves in such a manner that its distance from a fixed point is equal to its distance from a fixed line multiplied by a constant greater than one
A. Ellipse
B. Hyperbola
C. Parabola
D. Circle
Answer : B

30. If the masses of both the bodies, as shown in the below figure, are reduced to 50 percent, then tension in the string will be
A. Same
B. Half
C. Double
D. None of these
Answer : B

31. A ladder is resting on a smooth ground and leaning against a rough vertical wall. The force of friction will act
A. Towards the wall at its upper end
B. Away from the wall at its upper end
C. Downward at its upper end
D. Upward at its upper end
Answer : D

32. The wheels of a moving car possess
A. Potential energy only
B. Kinetic energy of translation only
C. Kinetic energy of rotation only
D. Kinetic energy of translation and rotation both
Answer : D

33. For any system of coplanar forces, the condition of equilibrium is that the
A. Algebraic sum of the horizontal components of all the forces should be zero
B. Algebraic sum of the vertical components of all the forces should be zero
C. Algebraic sum of moments of all the forces about any point should be zero
D. All of the above
Answer : D

34. A single force and a couple acting in the same plane upon a rigid body
A. Balance each other
B. Cannot balance each other
C. Produce moment of a couple
D. Are equivalent
Answer : B

35. A heavy string attached at two ends at same horizontal level and when central dip is very small approaches the following curve
A. Circular arc
B. Parabola
C. Hyperbola
D. Elliptical
Answer : B

36. The angle of inclination of the plane at which the body begins to move down the plane, is called
A. Angle of friction
B. Angle of repose
C. Angle of projection
D. None of these
Answer : A

37. A machine having an efficiency less than 50%, is known as
A. Reversible machine
B. Non-reversible machine
C. Neither reversible nor non-reversible machine
D. Ideal machine
Answer : B

38. The unit of force in S.I. units is
A. kilogram
B. Newton
C. Watt
D. Dyne
Answer : B

39. The maximum efficiency of a screw jack is
A. (1 - sin?)/(1 + sin?)
B. (1 + sin?)/(1 - sin?)
C. (1 - tan?)/(1 + tan?)
D. (1 + tan?)/(1 - tan?)
Answer : A

40. The moment of inertia of a thin spherical shell of mass m and radius r, about its diameter is
A. mr²/3
B. 2mr²/3
C. 2mr²/5
D. 3mr²/5
Answer : B

41. A particle moves along a straight line such that distance (x) traversed in t seconds is given by x = t² (t - 4), the acceleration of the particle will be given by the equation
A. 6t² - 8t
B. 3t² + 2t
C. 6f - 8
D. 6f - 4
Answer : C

42. Which of the following is a scalar quantity?
A. Force
B. Speed
C. Velocity
D. Acceleration
Answer : B

43. The maximum mechanical advantage of a lifting machine is
A. 1 + m
B. 1 - m
C. 1 / m
D. m
Answer : C

44. Non-coplanar non-concurrent forces are those forces which
A. Meet at one point, but their lines of action do not lie on the same plane
B. Do not meet at one point and their lines of action do not lie on the same plane
C. Do not meet at one point but their lines of action lie on the same plane
D. None of the above
Answer : B

45. One kg force is equal to
A. 7.8 N
B. 8.9 N
C. 9.8 N
D. 12 N
Answer : C

46. The time of flight (t) of a projectile on an upward inclined plane is (where u = Velocity of projection, ? = Angle of projection, and ? = Inclination of the plane with the horizontal.)
A. t = g cos ?/2u sin (? - ?)
B. t = 2u sin (? - ?)/g cos ?
C. t = g cos ?/2u sin (? + ?)
D. t = 2u sin (? + ?)/g cos ?
Answer : B

47. The centre of gravity of a uniform lamina lies at
A. The centre of heavy portion
B. The bottom surface
C. The midpoint of its axis
D. All of the above
Answer : C

48. The length of a second's pendulum is
A. 94.9 cm
B. 99.4 cm
C. 100 cm
D. 101 cm
Answer : B

49. The maximum frictional force, which comes into play, when a body just begins to slide over the surface of the other body, is known as
A. Static friction
B. Dynamic friction
C. Limiting friction
D. Coefficient of friction
Answer : C

50. Moment of inertia of a hollow circular section, as shown in the below figure about X-axis, is
A. ?/16 (D² - d²)
B. ?/16 (D³ - d³)
C. ?/32 (D? - d?)
D. ?/64 (D? - d?)
Answer : D