Applied Mechanics and Graphic Statics MCQ Solved Paper for GRE

1. Two circular discs of same weight and thickness are made from metals having different densities. Which disc will have the larger rotational inertia about its central axis?
A. Disc with larger density
B. Disc with smaller density
C. Both discs will have same rotational inertia
D. None of the above
Answer : B

2. One half of a vibration of a body, is called
A. Period time
B. Oscillation
C. Beat
D. Amplitude
Answer : C

3. For a simple pendulum, the period of one oscillation is
A. 2? ?(l/2g)
B. 2? ?(2g/l)
C. 2? ?(l/g)
D. 2? ?(g/2l)
Answer : C

4. If the gravitational acceleration at any place is doubled, the weight of a body, will
A. Be reduced to half
B. Be doubled
C. Not be affected
D. None of these
Answer : B

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

A. (h/3) × [(b + 2a)/(b + a)]
B. (h/3) × [(2b + a)/(b + a)]
C. (h/2) × [(b + 2a)/(b + a)]
D. (h/2) × [(2b + a)/(b + a)]
Answer : A

6. The angular speed of a car taking a circular turn of radius 100 m at 36 km/hr will be
A. 0.1 rad/sec
B. 1 rad/sec
C. 10 rad/sec
D. 100 rad/sec
Answer : A

7. 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

8. 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

9. The product of mass and velocity of a moving a body, is called
A. Moment
B. Momentum
C. Power
D. Impulse
Answer : B

10. The following statement is one of the laws of Dynamic friction
A. The force of friction always acts in a direction opposite to that in which a body is moving
B. The magnitude of the kinetic friction bears a constant ratio to the normal reaction between two surfaces. The ratio being slightly less than that in the case of limiting friction
C. For moderate speeds the force of friction remains constant but decreases slightly with the increase of speed
D. All the above
Answer : D

11. If a particle moves with a uniform angular velocity ? radians/sec along the circumference of a circle of radius r, the equation for the velocity of the particle, is
A. v = ? ?(y² - r²)
B. y = ? ?(y - r)
C. v = ? ?(r² + y²)
D. v = ? ?(r² - y²)
Answer : D

12. 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

13. Force polygon method is applicable for
A. Any coplanar force system
B. A system of parallel forces only
C. Concurrent coplanar force system
D. Non-concurrent coplanar force system
Answer : C

14. The ends of a string weighing w/metre are attached to two points at the same horizontal level. If the central dip is very small, the horizontal tension of the string throughout is
A. wl/4d
B. wl²/4d
C. wl²/8d
D. wl²/16d
Answer : C

15. 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
Answer : D

16. To avoid bending action at the base of a pier,
A. Suspension and anchor cables are kept at the same level
B. Suspension and anchor cables are fixed to pier top
C. Suspension cable and anchor cables are attached to a saddle mounted on rollers on top of the pier
D. None the these
Answer : B

17. If a set of given forces are such that their free vectors build a closed polygon, then
A. The resultant force and resultant couple are always zero
B. The resultant force is zero but resultant couple is not zero
C. The resultant force is zero but resultant couple may not be zero
D. The resultant force and resultant couple both may not be zero
Answer : C

18. 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

19. A particle of mass 2 kg executes simple harmonic motion of frequency 6/71 Hz and amplitude 0.25 m. Its maximum kinetic energy is
A. 4.5 J
B. 9.0 J
C. 12.0 J
D. 18.0 J
Answer : B

20. If G is the Gauge o 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 super elevation is
A. gv²/Gr
B. Gr²/gr
C. Gr²/gv²
D. Gv²/gv
Answer : D

21. The C.G. of a thin hollow cone of height h, above its base lies on the axis, at a height of
A. h/3
B. h/4
C. 2h/3
D. 3h/4
Answer : C

22. Maximum efficiency of a screw jack for the angle of friction ?, is
A. sin ?/(1 + sin ?)
B. (1 - sin ?)/sin ?
C. (1 + sin ?)/(1 - sin ?)
D. (1 - sin ?)/(1 + sin ?)
Answer : D

23. 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
Answer : A

24. 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

25. The direction of projection should bisect the angle between the inclined plane and the vertical for a range of a projectile on inclined plane
A. To be zero
B. To be maximum
C. To be minimum
D. None of these
Answer : B

26. A projectile is fired at an angle ? to the vertical. Its horizontal range will be maximum when ? is
A. 0°
B. 30°
C. 45°
D. 90°
Answer : C

27. 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

28. 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

29. 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
Answer : B

30. 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
Answer : D

31. A point subjected to a number of forces will be in equilibrium, if
A. Sum of resolved parts in any two directions at right angles, are both zero
B. Algebraic sum of the forces is zero
C. Two resolved parts in any two directions at right angles are equal
D. Algebraic sum of the moments of the forces about the point is zero
Answer : A

32. 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

33. Minimum potential energy of a system will be in the position of
A. Stable equilibrium
B. Unstable equilibrium
C. Neutral equilibrium
D. All of the above
Answer : A

34. Time of flight of a projectile on a horizontal plane, is
A. 2u sin?/g
B. 2u cos?/g
C. 2u tan?/g
D. 2u cot?/g
Answer : A

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

36. 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

37. 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

38. The motion of a particle moving with S.H.M. from an extremity to the other, constitutes
A. Half an oscillation
B. One full oscillation
C. Two oscillations
D. None of these
Answer : A

39. If the given forces P?, P?, P? and P? are such that the force polygon does not close, then the system will
A. Be in equilibrium
B. Always reduce to a resultant force
C. Always reduce to a couple
D. Both (A) and (C)
Answer : B

40 The unit of force in C.G.S. system of units, is called
A. Dyne
B. Newton
C. Kg
D. All the above
Answer : A

41. A bullet weighing 200 g is fired horizontally with a velocity of 25 m/sec from a gun carried on a carriage which together with the gun weighs 100 kg. The velocity of recoil of the gun, will be
A. 0.01 m/sec
B. 0.05 m/sec
C. 1.00 m/sec
D. 1.5 m/see
Answer : B

42. 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

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

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

44. In a simple harmonic motion, the position of equilibrium is always
A. Stable
B. Unstable
C. Neutral
D. None of the above
Answer : A

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

46. 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

47. If g1 and g2 are the gravitational accelerations on two mountains A and B respectively, the weight of a body when transported from A to B will be multiplied by
A. g1
B. g2
C. g1/g2
D. g2/g1
Answer : D

48. 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

49. 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

50. The intrinsic equation of catenary is
A. S = c tan ?
B. y = c cosh x/c
C. y = c cosh ?
D. y = c sinh ?
Answer : A