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1000+ Applied Mechanics and Graphic Statics MCQ for JEE Main [Solved]

Thursday 9th of March 2023

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1. 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
2. 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
3. u1 and u2 are the velocities of approach of two moving bodies in the same direction and their corresponding velocities of separation are v1 and v2. As per Newton's law of collision of elastic bodies, the coefficient of restitution (e) is given by
A. e = v1 - v2/u2 - u1
B. e = u2 - u1/v1 - v2
C. e = v2 - v1/u1 - u2
D. e = v1 - v2/u2 + u1
Answer : C
4. The ratio of the speed of a rolling cylinder to the speed of sliding cylinder is
A. Less than 1
B. Equal to 1
C. Between 1 and 2
D. Greater than 2
Answer : A
5. 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
6. 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
7. 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
8. 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
9. The C.G. of the shaded area of the below figure from the x-axis is
A. a/4
B. 3a/4
C. 3b/10
D. 3a/10
Answer : C
10. If A is the amplitude of particle executing simple harmonic motion, then the total energy E of the particle is
A. Proportional to A
B. Proportional to A²
C. Proportional to 1/A²
D. Independent of A
Answer : B
11. The reaction at the support B of the beam shown in below figure is
A. 1.6 t
B. 9.6 t
C. 8.5 t
D. 0.5 t
Answer : C
12. If two forces acting at a point are in equilibrium, they must be equal in magnitude and their line of action must be along
A. The same line in the same sense
B. The same line in opposite sense
C. The perpendicular to both the lines
D. None of these
Answer : B
13. A rigid body suspended vertically at a point and oscillating with a small amplitude under the action of the force of gravity, is called
A. Simple pendulum
B. Compound pendulum
C. Second's pendulum
D. None of these
Answer : B
14. The angle which an inclined surface makes with the horizontal when a body placed on it is on the point of moving down, is called
A. Angle of repose
B. Angle of friction
C. Angle of inclination
D. None of these
Answer : A
15. A ball moving on a smooth horizontal table hits a rough vertical wall, the coefficient of restitution between ball and wall being 1/3. The ball rebounds at the same angle. The fraction of its kinetic energy lost is
A. 1/3
B. 2/3
C. 1/9
D. 8/9
Answer : D
16. Instantaneous center is at infinity when the angular velocity is
A. Constant
B. Zero
C. Maximum
D. Minimum
Answer : B
17. The member forces in a statically in determinate truss
A. Can be obtained by graphic statics
B. Cannot be obtained by graphic statics
C. May be obtained by graphic statics
D. Can be obtained by graphic statics by trial and error
Answer : B
18. 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
19. An ordinate in a funicular polygon represents
A. Shear force
B. Resultant force
C. Bending moment
D. Equilibrium
Answer : C
20. 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
21. If a projectile is fired with an initial velocity of 10 m/sec at an angle of 60° to the horizontal, its horizontal and vertical velocity at the highest point of trajectory are
A. 0 and 5 m/sec
B. 5 m/sec and 0
C. 5?3 m/sec and 0
D. 5 and 5?3 m/sec
Answer : B
22. A force P of 50 N and another force Q of unknown magnitude act at 90° to each other. They are balanced by a force of 130 N. The magnitude of Q is
A. 60 N
B. 80 N
C. 100 N
D. 120 N
Answer : D
23. 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
24. For a given velocity of a projectile, the range is maximum when the angle of projection is
A. 30°
B. 45°
C. 90°
D. 0°
Answer : B
25. 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
26. A ball of mass 250 g moving on a smooth horizontal table with a velocity of 10 m/sec hits an identical stationary ball B on the table. If the impact is perfectly plastic, 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 : A
27. 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
28. The centre of gravity of a trapezoidal dam section whose top width is a, bottom width is band the vertical side is a, from its vertical face is
A. (a² + ab + b²)/3 (a + b)
B. (b² + bc + c²)/3 (b + c)
C. (a² + ab + c²)/3 (a + c)
D. None of these
Answer : A
29. 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
30. 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
31. 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 mechanical advantage of the lifting machine is
A. 15
B. 18
C. 20
D. 26
Answer : C
32. 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
33. A 2 m long ladder rests against a wall and makes an angle of 30° with the horizontal floor. Where will be the instantaneous center of rotation when the ladder starts slipping? (i) 1.0 in from the wall (ii) 1.732 m from the wall (iii) 1.0 m above the floor (iv) 1.732 m above the floor The correct answer is
A. (i) and (iii)
B. (i) and (iv)
C. (ii) and (iii)
D. (ii) and (iv)
Answer : D
34. 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
35. 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
36. If the angular distance, 0 = 2t3 - 3t², the angular acceleration at t = 1 sec. is
A. 1 rad/sec²
B. 4 rad/sec²
C. 6 rad/sec²
D. 12 rad/sec²
Answer : C
37. The load shared by the member BC of the structure shown in below figure is
A. 23 t
B. 32 t
C. 4 t
D. 3 t
Answer : C
38. Which of the following represents the state of neutral equilibrium?
A. A cube resting on one edge
B. A smooth cylinder lying on a curved surface
C. A smooth cylinder lying on a convex surface
D. None of the above
Answer : D
39. The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by
A. 1 : 2
B. 1 : 1
C. 2 : 1
D. 3 : 1
Answer : D
40. Three forces which act on a riid 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
41. 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
42. The masses of two balls are in the ratio of 2 : 1 and their respective velocities are in the ratio of 1 : 2 but in opposite direction before impact. If the coefficient of restitution is ½, the velocities of separation of the balls will be equal to
A. Original velocity in the same direction
B. Half the original velocity in the same direction
C. Half the original velocity in the opposite direction
D. Original velocity in the opposite direction
Answer : D
43. 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
44. If l is the span of a light suspension bridge whos each cable carries total weight (w) and the central dip is y, the horizontal pull at each support, is
A. wl/4y
B. wl/8y
C. wl/2y
D. wl
Answer : B
45. The force acting on a point on the surface of a rigid body may be considered to act
A. At the centre of gravity of the body
B. On the periphery of the body
C. On any point on the line of action of the force
D. At any point on the surface normal to the line of action of the force
Answer : C
46. The diagram showing the point of application and line of action of forces in their plane is called
A. Vector diagram
B. Space diagram
C. Force diagram
D. Funicular diagram
Answer : B
47. 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
48. 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
49. Work may be defined as
A. Force × distance
B. Force × velocity
C. Force × acceleration
D. None of these
Answer : A
50. Two loads of 50 kg and 75 kg are hung at the ends of a rope passing over a smooth pulley shown in below figure. The tension in the string is:
A. 50 kg
B. 75 kg
C. 25 kg
D. 60 kg
Answer : D
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