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Applied Mechanics and Graphic Statics MCQ Solved Paper for LSAT

Thursday 9th of March 2023

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1. M.I. of a thin ring (external diameter D, internal diameter d) about an axis perpendicular to the plane of the ring, is
A. ?/64 (D4 + d4)
B. ?/32 (D4 - d4)
C. ?/32 (D4 + d4)
D. ?/32 (D4 × d4)
Answer : B
2. 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
3. The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be
A. sin (? + ?)/sin (? - ?)
B. sin (? - ?)/sin (? + ?)
C. cos (? - ?)/cos (? + ?)
D. tan (? - ?)/tan (? + ?)
Answer : B
4. 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
5. Power can be expressed as
A. Work/energy
B. Work/time
C. Work × time
D. Work/distance
Answer : B
6. One Joule is equivalent to
A. 9.81 Newton metre
B. 1 Newton metre
C. 1 kg wt metre
D. 1 dyne metre
Answer : B
7. A 49 kg lady stands on a spring scale in an elevator. During the first 5 sec, starting from rest, the scale reads 69 kg. The velocity of the elevator will be
A. 10 m/sec
B. 15 m/sec
C. 20 m/sec
D. 25 m/sec
Answer : C
8. 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
9. A cable loaded with 0.5 tonne per horizontal metre span is stretched between supports in the same horizontal line 400 m apart. If central dip is 20 m, the minimum tension in the cable, will be
A. 200 tonnes at the centre
B. 500 tonnes at the centre
C. 200 tonnes at the right support
D. 200 tonnes at the left support
Answer : B
10. For the system of the loads shown in below figure, the time required for the 6.6 kg load to fall on the edge, is
A. 1 sec
B. 2 sec
C. 3 sec
D. 4 sec
Answer : C
11. 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
12. The acceleration of a train starting from rest at any instant is 1/6(V + 1) m/sec² where V is the velocity of the train in m/sec. The train will attain a velocity of 36 km/hour after travelling a distance of
A. 2000 m
B. 2100 m
C. 2200 m
D. 2300 m
Answer : D
13. The resultant of two forces acting at right angles is 5 kgf and if they act at an angle of 60°, it is 37 kgf. The magnitudes of the forces are:
A. 2 kgf, 3 kgf
B. 3 kgf, 4 kgf
C. 4 kgf, 5 kgf
D. 5 kgf, 3 kgf
Answer : B
14. The numbers of funicular polygons which can be drawn to pass through two specified points in the space diagram are
A. Zero
B. 1
C. 2
D. Infinity
Answer : D
15. The centre of gravity of a triangle is at the point where three
A. Medians of the triangle meet
B. Perpendicular bisectors of the sides of the triangle meet
C. Bisectors of the angle of the triangle meet
D. None of these
Answer : A
16. In simple harmonic motion, acceleration of a particle is proportional to
A. Rate of change of velocity
B. Displacement
C. Velocity
D. Direction
Answer : B
17. 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
18. Which of the following is a scalar quantity?
A. Energy
B. Momentum
C. Torque
D. Impulse
Answer : A
19. A particle is executing simple harmonic motion in a line 1.0 m long. If the time of one complete vibration is 1 sec, then the maximum velocity of the particle is
A. 1.00 m/sec
B. 1.57 m/sec
C. 3.14 m/sec
D. 6.28 m/sec
Answer : C
20. 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
21. 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
22. 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
23. 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
24. In a lifting machine with efficiency 60%, an effort of 200 N is required to raise a load of 6 kN. The velocity ratio of the machine is
A. 30
B. 50
C. 60
D. 80
Answer : B
25. 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
26. 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
27. The total time of collision and restitution of two bodies, is called
A. Time of collision
B. Period of collision
C. Period of impact
D. All the above
Answer : D
28. 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
29. If the kinetic energy and potential energy of a simple harmonic oscillator of amplitude A are both equal to half the total energy, then the displacement is equal to
A. A
B. A/2
C. A/?2
D. A?2
Answer : C
30. 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
31. Centre of gravity of a thin hollow cone lies on the axis of symmetry at a height of
A. One-half of the total height above base
B. One-third of the total height above base
C. One-fourth of the total height above base
D. None of these
Answer : B
32. The point about which combined motion of rotation and translation of a rigid body takes place, is known as
A. Virtual centre
B. Instantaneous centre
C. Instantaneous axis
D. Point of rotation
Answer : B
33. One end of an elastic string of natural length / and modulus X is kept fixed while to the other end is attached a particle of mass m which is hanging freely under gravity. The particle is pulled down vertically through a distance x, held at rest and then released. The motion is
A. A simple harmonic motion
B. A rectilinear motion with constant speed
C. A damped oscillatory motion
D. None of the above
Answer : A
34. Pick up the correct statement from the following:
A. If two equal and perfectly elastic smooth spheres impinge directly, they interchange their velocities
B. If a sphere impinges directly on an equal sphere which is at rest, then a fraction ½(1 - e2) the original kinetic energy is lost by the impact
C. If two equal spheres which are perfectly elastic impinge at right angles, their direction after impact will still be at right angles
D. All the above
Answer : D
35. Kinetic friction may be defined as
A. Friction force acting when the body is just about to move
B. Friction force acting when the body is in motion
C. Angle between normal reaction and resultant of normal reaction and limiting friction
D. Ratio of limiting friction and normal reaction
Answer : B
36. A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If r is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be
A. [r (? + 0.25)]/(? - 0.5)
B. [r (? - 0.5)]/(? + 0.25)
C. [r (? - 0.25)]/(? - 0.5)
D. [r (? + 0.25)]/(? + 0.5)
Answer : C
37. 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
38. The locus of the instantaneous centre of a moving rigid body, is
A. Straight line
B. Involute
C. Centroid
D. Spiral
Answer : C
39. 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
40. Pick up the incorrect statement from the following. In a smple harmonic motion
A. Velocity is maximum at its mean position
B. Velocity is minimum at the end of the stroke
C. Acceleration is minimum at the end of the stroke
D. Acceleration is zero at the mean position
Answer : C
41. 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. 8°
B. 9°
C. 10°
D. 11°
Answer : C
42. A glass ball is shot to hit a wall from a point on a smooth floor. If the ball returns back to the point of projection in twice the time taken in reaching the wall, the coefficient of restitution between the glass ball and the wall is
A. 0.25
B. 0.33
C. 0.40
D. 0.50
Answer : D
43. Newtons Law of Motion is:
A. Everybody continues in its state of rest or of uniform motion in a straight line, unless it is acted upon by some external force
B. The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts
C. To every action, there is always an equal and opposite reaction
D. All the above
Answer : D
44. The piston of a steam engine moves with a simple harmonic motion. The crank rotates 120 r.p.m. and the stroke length is 2 metres. The linear velocity of the piston when it is at a distance of 0.5 metre from the centre, is
A. 5.88 m/sec
B. 8.88 m/sec
C. 10.88 m/sec
D. 12.88 m/sec
Answer : C
45. The force polygon representing a set of forces in equilibrium is a
A. Triangle
B. Open polygon
C. Closed polygon
D. Parallelogram
Answer : C
46. 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
47. 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
48. 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
49. A rod 5 m in length is moving in a vertical plane. When it is inclined at 60° to horizontal, its lower end is moving horizontally at 3 m/sec and upper end is moving in vertical direction. The velocity of its upper end, is
A. 0.5 m/sec
B. 1.0 m/sec
C. 1.5 m/sec
D. 2.5 m/sec
Answer : B
50. 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
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