GATE - Applied Mechanics and Graphic Statics 1000+ MCQ [Solved] PDF Download

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

2. Joule is the unit of
A. Power
B. Impulse
C. Work
D. Momentum
Answer : C

3. 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

4. The maximum displacement of a particle executing S.H.M. corresponds to
A. Zero potential energy and maximum kinetic energy
B. Zero kinetic energy and maximum potential energy
C. Maximum kinetic energy and maximum potential energy
D. Minimum kinetic energy and minimum potential energy
Answer : B

5. A heavy ladder resting on a floor and against a vertical wall may not be in equilibrium, if
A. Floor is smooth and the wall is rough
B. Floor is rough and the wall is smooth
C. Floor and wall both are smooth surfaces
D. Floor and wall both are rough surfaces
Answer : C

6. 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

7. An ordinate in a funicular polygon represents
A. Shear force
B. Resultant force
C. Bending moment
D. Equilibrium
Answer : C

8. The resultant of two forces P and Q acting at an angle ?, is
A. P² + Q² + 2P sin ?
B. P² + Q² + 2PQ cos ?
C. P² + Q² + 2PQ tan ?
D. ?(P² + Q² + 2PQ cos ?)
Answer : D

9. When a body in equilibrium undergoes an infinitely small displacement, work imagined to be done, is known as
A. Imaginary work
B. Negative work
C. Virtual work
D. None of these
Answer : C

10. It is observed that in a certain sinusoidal oscillation, the amplitude is linearly dependent on the frequency f. If the maximum velocity during the oscillation is V, then V must be proportional to
A. f
B. 1/f
C. 1/f²
D. f²
Answer : D

11. 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
Answer : D

12. A rigid body is in a stable equilibrium if the application of any force
A. Can raise the CG of the body but cannot lower it
B. Tends to lower the CG of the body
C. Neither raises nor lowers the CG of the body
D. None of above
Answer : A

13. 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

14. 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

15. In SI units, the units of force and energy are respectively
A. Newton and watt
B. Dyne and erg
C. Newton and joule
D. kg wt and joule
Answer : C

16. A Seconds pendulum executes
A. 0.5 beat per second
B. 1.0 beat per second
C. 2.0 beats per second
D. 2.5 beats per second
Answer : C

17. 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
Answer : D

18. A ladder of weight 'w' rests against a smooth vertical wall, and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being 1/4. The maximum angle of inclination of the ladder to the vertical, if a man of weight 'w' is to walk to the top of it safely, is tan'1 x, where x is
A. 1/4
B. 1/3
C. 3
D. 4
Answer : B

19. A system of coplanar forces is in equilibrium when
A. Force polygon closes
B. Funicular polygon closes
C. Both force polygon and funicular polygon close
D. All the forces are concurrent
Answer : C

20. The beam shown in below figure is supported by a hinge at A and a roller at B. The reaction RA of the hinged support A of the beam, is
A. 10.8 t
B. 10.6 t
C. 10.4 t
D. 10.2 t
Answer : D

21. 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
Answer : A

22. When a circular wheel rolls on a straight track, then the shape of body centrode and space centrode respectively are
A. Straight line and parabola
B. Straight line and circle
C. Circle and straight line
D. Circle and parabola
Answer : C

23. The angles between two forces to make their resultant a minimum and a maximum respectively are
A. 0° and 90°
B. 180° and 90°
C. 90° and 180°
D. 180° and 0°
Answer : D

24. The Law of Polygon of Forces states that
A. If a polygon representing the forces acting at point in a body is closed, the forces are in equilibrium
B. If forces acting on a point can be represented in magnitude and direction by the sides of a polygon taken in order, then the resultant of the forces will be represented in magnitude and direction by the closing side of the polygon
C. If forces acting on a point can be represented of a polygon taken in order, their sides of a polygon taken in order, their resultant will be represented in magnitude and direction by the closing side of the polygon, taken in opposite order
D. If forces acting on a point can be represented in magnitude and direction by the sides of a polygon in order, the forces are in equilibrium
Answer : C

25. Time period and length of a seconds pendulum respectively are
A. 1 sec and 99.4 cm
B. 1 sec and 92.7 cm
C. 2 sec and 99.4 cm
D. 2 sec and 92.7 cm
Answer : C

26. From a solid cylinder of height 8 cm and radius 4 cm, a right circular cone is scooped out on the same base and having the same height as that of the cylinder. The C.G. of the remainder is at a height of
A. 4.5 cm
B. 5.0 cm
C. 5.25 cm
D. 5.5 cm
Answer : B

27. Instantaneous center is at infinity when the angular velocity is
A. Constant
B. Zero
C. Maximum
D. Minimum
Answer : B

28. If a spherical body is symmetrical about its perpendicular axes, the moment of inertia of the body about an axis passing through its centre of gravity as given by Routh's rule is obtained by dividing the product of the mass and the sum of the squares of two semi-axes by n. Where, n is
A. 2
B. 3
C. 4
D. 5
Answer : D

29. When a body falls freely under gravitational force, it possesses
A. Maximum weight
B. Minimum weight
C. No weight
D. No effect on its weight
Answer : C

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

31. 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

32. 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

33. 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

34. 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 mean position
C. Through a point at half amplitude
D. None of these
Answer : B

35. 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. ¾ l
B. ½ l
C. l/?2
D. 2/?3 l
Answer : C

36. If the angle between the applied force and the direction of motion of a body, is between 90° and 180°, the work done, is called
A. Virtual work
B. Imaginary work
C. Zero work
D. Negative work
Answer : D

37. A retarding force on a body does not
A. Change the motion of the body
B. Retard the motion of the body
C. Introduce the motion of the body
D. None of these
Answer : B

38. A funicular polygon cannot be made to pass through
A. One specified point
B. Two specified points
C. Three specified points
D. More than three specified points
Answer : D

39. The unit of Moment of Inertia of a body, is
A. m
B. m²
C. m³
D. m⁴
Answer : D

40. For a simple pendulum, time period for a beat, is
A. ? ?(l/g)
B. ? ?(2l/g)
C. ? ?(g/2l)
D. ? ?(l/2g)
Answer : A

41. The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be
A. 30°
B. 45°
C. 60°
D. 75°
Answe : D

42. One end of a light string 4 m in length is fixed to a point on a smooth wall and the other end fastened to a point on the surface of a smooth sphere of diameter 2.25 m and of weight 100 kg. The reaction between the sphere and the wall of the arrangement made is
A. 102.5 kg
B. 105.5 kg
C. 108.5 kg
D. 110 kg
Answer : A

43. If the tension in a cable supporting a lift moving upwards is twice the tension when the lift is moving downwards, the acceleration of the lift, is
A. g/2
B. g/3
C. g/4
D. g/5
Answer : B

44. 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:
A. 40 g
B. 60 g
C. 80 g
D. 100 g
Answer : C

45. 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)
Answer : D

46. 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

47. The velocity ratio of an inclined plane of inclination ? with horizontal for lifting a load is
A. sin ?
B. cos ?
C. tan ?
D. cosec ?
Answer : D

48. The maximum frictional force which comes into play, when a body just begins to slide over the surface of a another body, is known
A. Sliding friction
B. Rolling friction
C. Limiting friction
D. None of these
Answer : C

49. 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 efficiency of the lifting machine is
A. 50 %
B. 40 %
C. 55 %
D. 30 %
Answer : A

50. If v and ? are linear and angular velocities, the centripetal acceleration of a moving body along the circular path of radius r, will be
A. r/v²
B. v²/r
C. r/?²
D. ?²/r
Answer : B