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1000+ Applied Mechanics and Graphic Statics MCQ for SSC JE [Solved]

Thursday 9th of March 2023

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1. The units of inertia of mass are
A. kg/m
B. kg/m2
C. m4
D. kg-m2
Answer : D
2. For lifting a load of 50 kg through a distance of 2.5 cm, an effort of 12.5 kg is moved through a distance of 40 cm. The efficiency of the lifting machine, is
A. 60 %
B. 65 %
C. 70 %
D. 75 %
Answer : D
3. If the angle of projection is double the angle of inclination (?) of the plane on which particle is projected, the ratio of times of flight up the inclined plane and down the inclined plane, will be
A. ½ cos ?
B. ½ sin ?
C. ½ tan ?
D. 2 cos ?
Answer : A
4. The practical units of work, is
A. Erg
B. Joule
C. Newton
D. Dyne
Answer : B
5. 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
6. A sphere and a cylinder having the same mass and radii start from rest and roll down the same inclined plane. Which body gets to the bottom first?
A. Sphere with greater rotational energy at bottom than cylinder
B. Sphere with lesser rotational energy at bottom than cylinder
C. Cylinder with greater rotational energy at bottom than sphere
D. Both reach the bottom simultaneously with equal rotational energy at bottom
Answer : B
7. 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
8. Which one of the following statements is true?
A. The tangent of the angle of friction is equal to coefficient of friction
B. The angle of repose is equal to angle of friction
C. The tangent of the angle of repose is equal to coefficient of friction
D. All the above
Answer : D
9. 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
10. If ? and u are the angle of projection and initial velocity of a projectile respectively, the horizontal range of the projectile, is
A. u² sin ?/g
B. u² sin² ?/g
C. u² sin ?/2g
D. u² sin² ?/2g
Answer : A
11. A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
A. Floor is smooth and wall is rough
B. Floor is rough and wall is smooth
C. Both floor and wall are rough
D. Both floor and wall are smooth
Answer : D
12. 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
13. 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
14. 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
15. A simple pendulum of length 1 has an energy E when its amplitude is A. If its amplitude is increased to 2 A, the energy becomes
A. E
B. E/2
C. 2E
D. 4E
Answer : D
16. 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
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. 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
19. The maximum velocity of a body vibrating with a simple harmonic motion of amplitude 150 mm and frequency 2 vibrations/sec, is
A. 188.5 m/sec
B. 18.85 m/sec
C. 1.885 m/sec
D. 0.18845 m/sec
Answer : C
20. 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
21. On a mass m describing a circular path of radius r, the centrifugal force
A. Acts tangentially to the circular path
B. Acts towards the centre of rotation
C. Acts away from the centre of rotation
D. Is mw2r/g kgf
Answer : B
22. The reaction at the support D of the continuous beam ABCD, hinged at two points shown in below figure is
A. 1.6 t ?
B. 1.6 t ?
C. 0.5 t ?
D. 0.5 t ?
Answer : B
23. A body is said to move with Simple Harmonic Motion if its acceleration, is
A. Always directed away from the centre, the point of reference
B. Proportional to the square of the distance from the point of reference
C. Proportional to the distance from the point of reference and directed towards it
D. Inversely proportion to the distance from the point of reference
Answer : C
24. Time required to stop a car moving with a velocity 20 m/sec within a distance of 40 m, is
A. 2 sec
B. 3 sec
C. 4 sec
D. 5 sec
Answer : C
25. A ball which is thrown upwards, returns to the ground describing a parabolic path during its flight
A. Vertical component of velocity remains constant
B. Horizontal component of velocity remains constant
C. Speed of the ball remains constant
D. Kinetic energy of the ball remains constant
Answer : B
26. ? rad/sec is the angular velocity of a crank whose radius is r. If it makes ?° with inner dead centre and obliquity of the connecting rod l is ?, the velocity v of the piston, is given by the equation
A. ?2 (l cos ? + r sin ? tan ?)
B. ?2 (l sin ? + r cos ? tan ?)
C. ? (l sin ? + r cos ? tan ?)
D. ?2 (l sin ? - r cos ? tan ?)
Answer : C
27. 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
28. The velocity ratio of the differential wheel and axle is
A. R/r1 - r2
B. 2R/r1
C. 3R/r1 - r2
D. 2R/r1 + r2
Answer : B
29. The displacement of a particle which moves along a straight line is given by S = 4t3 + 3t2- 10 where S is in meters and t is in seconds. The time taken by the particle to acquire a velocity of 18 m/sec from rest, is
A. ½ sec
B. 1 sec
C. 1.2 sec
D. 1.5 sec
Answer : B
30. A rod AB carries three loads of 30 N, 70 N and 100 N at distances of 20 mm, 90 mm and 150 mm respectively from A. Neglecting the weight of the rod, the point at which the rod will balance is
A. 109.5 mm from A
B. 119.5 mm from A
C. 125.5 mm from A
D. 132.5 mm from A
Answer : A
31. 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
32. Which one of the following laws is not applicable to a simple pendulum?
A. The time period does not depend on its magnitude
B. The time period is proportional to its length l
C. The time period is proportional to l, where l is length
D. The time period is inversely proportional to g, where g is the acceleration due to gravity
Answer : B
33. 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
34. 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.
B.
C. 10°
D. 11°
Answer : C
35. 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
36. 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
37. At the instantaneous center, the velocity of the moving lamina at any instant is
A. Zero
B. Maximum
C. Minimum
D. Varying
Answer : A
38. 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
39. A disc of mass 4 kg, radius 0.5 m and moment of inertia 3 kgm² rolls on a horizontal surface so that its center moves with speed 5 m/see. Kinetic energy of the disc is
A. 50 J
B. 150 J
C. 200 J
D. 400 J
Answer : C
40. A bullet weighing 10 gm moves with a velocity of l km/sec. Its kinetic energy i (i) 5000 Nm (ii) 5000 kg.m (iii) 5000 J The correct answer is
A. Only (ii)
B. Both (i) and (iii)
C. Both (ii) and (iii)
D. All (i), (ii) and (iii)
Answer : B
41. A shell travelling with a horizontal velocity of 100 m/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan1 x, where x is
A. 3/4
B. 4/5
C. 5/3
D. 3/5
Answer : D
42. 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
43. When a body slides down an inclined surface, the acceleration (f) of the body, is given by
A. f = g
B. f = g sin ?
C. f = g cos ?
D. f = g tan ?
Answer : B
44. 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
45. 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
46. If the velocity of projection is 4 m/sec and the angle of projection is ?°, the maximum height of the projectile from a horizontal plane, is
A. u² cos² ?/2g
B. u² sin² ?/2g
C. u² tan² ?/2g
D. u² sin 2?/2g
Answer : B
47. 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
48. In a simple harmonic motion, the position of equilibrium is always
A. Stable
B. Unstable
C. Neutral
D. None of the above
Answer : A
49. A cable loaded with 10 kN/m of span is stretched between supports in the same horizontal line 100 m apart. If the central dip is 10 m, then the maximum and minimum pull in the cable respectively are
A. 1346.3 kN and 1500 kN
B. 1436.2 kN and 1250 kN
C. 1346.3 kN and 1250 kN
D. 1436.2 kN and 1500 kN
Answer : C
50. 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

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