1000+ Applied Mechanics and Graphic Statics Multiple Choice Question Answer [Solved]

1. Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m/sec and 1 m/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is
A. 2/3
B. 1/5
C. 3/5
D. 1/3
Answer : B

2. 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

3. A particle moves in a straight line and its position is defined by the equation x = 6 t² - t³ where t is expressed in seconds and x in meters. The maximum velocity during the motion is
A. 6 m/sec
B. 12 m/sec
C. 24 m/sec
D. 48 m/sec
Answer : B

4. 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

5. 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

6. A particle moves along a straight line such that distance x traversed in t seconds is given by x = t2(t + 1), the acceleration of the particle, will be
A. 3t³ - 2t
B. 3t² + 2t
C. 6t - 2
D. 6t + 2
Answer : D

7. If two forces are in equilibrium, then the forces must (i) Be equal in magnitude (ii) Be opposite in sense (iii) Act along the same line The correct answer is
A. (i) and (ii)
B. (i) and (iii)
C. Only (i)
D. All (i), (ii) and (iii)
Answer : D

8. 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

9. A particle is dropped from a height of 3 m on a horizontal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the ball will rebound after striking the floor is
A. 0.5 m
B. 0.75 m
C. 1.0 m
D. 1.5 m
Answer : B

10. 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

11. 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

12. Effect of a force on a body depends upon its
A. Direction
B. Magnitude
C. Position
D. All the above
Answer : D

13. When a body moves round a fixed axis, it has
A. A rotary motion
B. A circular motion
C. A translatory
D. A rotary motion and translatory motion
Answer : B

14. The length of a Second's pendulum, is
A. 99.0 cm
B. 99.4 cm
C. 100 cm
D. 101 cm
Answer : B

15. If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is
A. Zero
B. Maximum
C. Minimum
D. None of these
Answer : B

16. To attain the synchronous orbit, the launch of a satellite, is done from a place
A. On equator
B. On 30° latitude
C. On 45° latitude
D. On the poles
Answer : A

17. 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

18. P is the force acting on a body whose mass is m and acceleration is f. The equation P - mf= 0, is known as
A. Equation of dynamics
B. Equation of dynamic equilibrium
C. Equation of statics
D. None of these
Answer : A

19. The moment of inertia of a hollow circular section whose external diameter is 8 cm and internal diameter is 6 cm, about centroidal axis, is
A. 437.5 cm⁴
B. 337.5 cm⁴
C. 237.5 cm⁴
D. 137.5 cm⁴
Answer : D

20. 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

21. 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

22. 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

23. 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

24. According to Kennedy's theorem, if three bodies have plane motions, their instantaneous centres lie on
A. A point
B. A straight line
C. Two straight lines
D. A triangle
Answer : B

25. 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

26. The gravitational force makes a satellite go round the earth in a circular orbit, if it is projected with an initial velocity of
A. 8.04 km/sec at a height of 285 km
B. 11.11 km/sec at a height of 37,400 km
C. 11.26 km/sec, the satellite escapes the pull of the earth
D. All the above
Answer : D

27. The units of moment of inertia of an area are
A. kg/m
B. kg/m²
C. m⁴
D. m³
Answer : C

28. A Seconds pendulum executes
A. 0.5 beat per second
B. 1.0 beat per second
C. 2.0 beats per second
D. 2.5 beats per second
Answer : C

29. The practical units of work, is
A. Erg
B. Joule
C. Newton
D. Dyne
Answer : B

30. The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be
A. 30°
B. 45°
C. 60°
D. 75°
Answer : D

31. At a given instant ship A is travelling at 6 km/h due east and ship B is travelling at 8 km/h due north. The velocity of B relative to A is
A. 7 km/hrs
B. 2 km/hrs
C. 1 km/hrs
D. 10 km/hrs
Answer : D

32. 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

33. M.I. of solid sphere, is
A. ? Mr²
B. ½ Mr²
C. Mr²
D. ?r⁴/2
Answer : C

34. 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

35. For a body moving with simple harmonic motion, the number of cycles per second, is known as its
A. Oscillation
B. Amplitude
C. Periodic time
D. Frequency
Answer : D

36. Angular acceleration of a particle may be expressed as
A. Radians/sec²
B. Degrees/sec²
C. Revolutions/sec
D. All the above
Answer : D

37. 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

38. A body of weight 14 g appears to weight 13 g when weighed by a spring balance in a moving lift. The acceleration of the lift at that moment was
A. 0.5 m/sec²
B. 0.7 m/sec²
C. 1 m/sec²
D. 1 cm/sec²
Answer : B

39. 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

40. Time period and length of a seconds pendulum respectively are
A. 1 sec and 99.4 cm
B. 1 sec and 92.7 cm
C. 2 sec and 99.4 cm
D. 2 sec and 92.7 cm
Answer : C

41. To double the period of oscillation of a simple pendulum
A. The mass of its bob should be doubled
B. The mass of its ob should be quadrupled
C. Its length should be quadrupled
D. Its length should be doubled
Answer : C

42. 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

43. 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

44. 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

45. ? 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

46. An ordinate in a funicular polygon represents
A. Shear force
B. Resultant force
C. Bending moment
D. Equilibrium
Answer : C

47. If G is the Gauge of 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

48. 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

49. 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

50. If a body is lying on a plane whose inclination with the horizontal is less than the angle of friction, then? (i) A force is required to move the body upwards (ii) A force is required to move the body downward (iii) The body will not be in equilibrium The correct answer is
A. Only (i)
B. Only (ii)
C. Both (i) and (ii)
D. Both (i) and (iii)
Answer : C