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1000+ Applied Mechanics and Graphic Statics MCQ for UPSC IES [Solved]

Thursday 9th of March 2023

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1. Pick up the correct statement from the following. The kinetic energy of a body
A. Before impact is equal to that after impact
B. Before impact is less than that after impact
C. Before impact is more than that after impact
D. Remain constant
Answer : C
2. The unit of Moment of Inertia of a body, is
A. m
B. m2
C. m3
D. m4
Answer : D
3. Williot-Mohr diagram is used to determine deflection in
A. Trusses only
B. Beam only
C. Rigid frames only
D. Any type of structure
Answer : A
4. 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
5. 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
6. 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 velocity ratio of the lifting machine is
A. 50
B. 55
C. 60
D. 65
Answer : A
7. 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
8. Two parallel forces 20 kg and 15 kg act. In order that the distance of the resultant from 20 kg force may be the same as that of the former resultant was from 15 kg, the 20 kg force is diminished by
A. 5.5 kg
B. 6.25 kg
C. 8.75 kg
D. 10.5 kg
Answer : C
9. 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
10. One Newton is equivalent to
A. 1 kg. wt
B. 9.81 kg. wt
C. 981 dyne
D. 1/9.81 kg. wt
Answer : D
11. A stone was thrown vertically upwards from the ground with a velocity of 50 m/sec. After 5 seconds another stone was thrown vertically upwards from the same place. If both the stones strike the ground at the same time, then the velocity with which the second stone was thrown should be (Assume g = 10 m/sec²)
A. 15 m/sec
B. 25 m/sec
C. 40 m/sec
D. 50 m/sec
Answer : B
12. 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
13. 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
14. A block of weight 50 kg is placed on a horizontal plane. When a horizontal force of 18 kg is applied, the block is just on the point of motion. The angle of friction is
A. 17° 48'
B. 18° 48'
C. 19° 48'
D. 20° 48'
Answer : C
15. 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
16. The length of a Second's pendulum, is
A. 99.0 cm
B. 99.4 cm
C. 100 cm
D. 101 cm
Answer : B
17. A stone is thrown up a slope of inclination 60° to the horizontal. At what angle to the slope must the stone be thrown so as to land as far as possible from the point of projection?
A. 15°
B. 30°
C. 45°
D. 75°
Answer : A
18. The C.G. of a hemisphere from its base measured along the vertical radius is at a distance of
A. 4R/3?
B. 3R/8
C. 3?R/4
D. 8R/3
Answer : B
19. The horizontal reaction at the support A of the structure shown in below figure, is

A. Zero
B. 2 t
C. 3 t
D. 1 t
Answer : A
20. 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
1. Pick up the incorrect statement from the following. In case of suspension bridge due to rise in temperature,
A. Dip of the cable increases
B. Length of the cable increases
C. Dip of the cable decreases
D. None of these
Answer : C
22. If ? and u are angle of projection and initial velocity of a projectile respectively, the total time of flight, is given by
A. T = u sin 2?/g
B. T = u sin²?/g
C. T = u sin²?/2g
D. T = 2u sin?/g
Answer : D
23. 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
24. 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
25. A cube on a smooth horizontal surface
A. Cannot be in stable equilibrium
B. Cannot be in neutral equilibrium
C. Cannot be in unstable equilibrium
D. Can be in any of these states
Answer : D
26. The moment of inertia of a circular lamina of diameter d, about an axis perpendicular to the plane of the lamina and passing through its centre, is
A. ?d4/12
B. ?d4/16
C. ?d4/24
D. ?d4/32
Answer : D
27. 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
28. 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
29. The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, is
A. 1/4
B. 1/2
C. 3/4
D. 2
Answer : A
30. A stone is whirled in a vertical circle, the tension in the string, is maximum
A. When the string is horizontal
B. When the stone is at the highest position
C. When the stone is at the lowest position
D. At all the positions
Answer : C
31. 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
32. A projectile is fired at an angle ? to the vertical. Its horizontal range will be maximum when ? is
A.
B. 30°
C. 45°
D. 90°
Answer : C
33. The units of moment of inertia of an area are
A. kg/m
B. kg/m2
C. m4
D. m3
Answer : C
34. The time period of a simple pendulum depends on (i) Mass of suspended particle (ii) Length of the pendulum (iii) Acceleration due to gravity The correct answer is
A. Only (i)
B. Both (ii) and (iii)
C. Both (i) and (iii)
D. All are correct
Answer : B
35. 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
36. Rate of change of angular momentum is equal to
A. Force
B. Torque
C. Linear momentum
D. Impulse
Answer : B
37. Two forces act an angle of 120°. If the greater force is 50 kg and their resultant is perpendicular to the smaller force, the smaller force is
A. 20 kg
B. 25 kg
C. 30 kg
D. 35 kg
Answer : B
38. 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
39. 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
40. 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
4. A light rope is loaded with many equal weights at equal horizontal intervals. The points of suspension on the rope lie on a
A. Parabola
B. Catenary
C. Cycloid
D. Ellipse
Answer : A
42. 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
43. If two forces P and Q (P > Q) act on the same straight line but in opposite direction, their resultant, is
A. P + Q
B. P/Q
C. Q/P
D. P - Q
Answer : D
44. The ratio of the reactions RA and RB of a simply supported beam shown in below figure is
A. 0.50
B. 0.40
C. 0.67
D. 1.00
Answer : D
45. The tension in a cable supporting a lift
A. Is more when the lift is moving downwards
B. Is less when the lift is moving upwards
C. Remains constant whether its moves downwards or upwards
D. Is less when the lift is moving downwards
Answer : D
46. A ball is dropped from a height of 16 m on a horizontal floor. If it rebounds to a height of 9 m after striking the floor, the coefficient of restitution between ball and floor is
A. 1/4
B. 2/3
C. 3/4
D. 4/3
Answer : C
47. 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
48. 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
49. The total kinetic energy of a hoop of mass 2 kg and radius 4 m sliding with linear velocity 8 m/sec and angular velocity 5 radian/sec is
A. 64 J
B. 400 J
C. 464 J
D. 89 J
Answer : C
50. To double the period of oscillation of a simple pendulum
A. The mass of its bob should be doubled
B. The mass of its bob should be quadrupled
C. Its length should be quadrupled
D. Its length should be doubled
Answer : C

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