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

1. From a circular plate of a diameter 6 cm is cut out a circle whose diameter is equal to the radius of the plate. The C.G. of the remainder from the centre of circular plate is at a distance of
A. 2.0 cm
B. 1.5 cm
C. 1.0 cm
D. 0.5 cm
Answer : D

2. The equation of motion of a particle starting from rest along a straight line is x = t³ - 3t²+ 5. The ratio of the accelerations after 5 sec and 3 sec will be
A. 2
B. 3
C. 4
D. 5
Answer : @

3. 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

4. Principle of Transmissibility of Forces states that, when a force acts upon a body, its effect is
A. Maximum if it acts at the centre of gravity of the body
B. Different at different points on its line of
C. Same at every point on its line of action
D. Minimum if it acts at the C.G. of the body
Answer : C

5. 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

6. When a body falls freely under gravitational force, it possesses
A. Maximum weight
B. Minimum weight
C. No weight
D. No effect on its weight
Answer : C

7. For a simple pendulum, time period for a beat, is
A. ? ?(l/g)
B. ? ?(2l/g)
C. ? ?(g/2l)
D. ? ?(l/2g)
Answer : A

8. 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

9. 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

10. 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

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

12. 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

13. 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

14. 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

15. 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

16. 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

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

18. A projectile is fired at an angle ? to the vertical. Its horizontal range will be maximum when ? is
A. 0°
B. 30°
C. 45°
D. 90°
Answer : C

19. One Newton force, is
A. 10³ dynes
B. 10⁴ dynes
C. 10⁵ dynes
D. 10⁶ dynes
Answer : C

20. 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
strong>D. 0.50
Answer : D

21. 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

22. A particle executes a simple harmonic motion. While passing through the mean position, the particle possesses
A. Maximum kinetic energy and minimum potential energy
B. Maximum kinetic energy and maximum potential energy
C. Minimum kinetic energy and maximum potential energy
D. Minimum kinetic, energy and minimum potential energy
Answer : A

23. 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 mw^2r/g kgf
Answer : B

24. A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its centre of mass has a speed of 200 mm/sec. The work required to stop the hoop is
A. 2 J
B. 4 J
C. 6 J
D. 8 J
Answer : B

25. The unit of impulse, is
A. kg.m/sec
B. kg.m/sec
C. kg.m/sec²
D. kg.m/sec
Answer : A

26. 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

27. 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

28. A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is
A. n rpm
B. n/2 rpm
C. n/4 rpm
D. 2n rpm
Answer : B

29. A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan1 x, where x is (Assume g = 10 m/sec²)
A. 3/8
B. 1/2
C. 9/5
D. 5/8
Answer : D

30. 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

31. The unit of moments in M.K.S system, is
A. kg.m
B. kg/m²
C. kg/sec²
D. kg/sec
Answer : A

32. A rigid body is in a stable equilibrium if the application of any force
A. Can raise the CG of the body but cannot lower it
B. Tends to lower the CG of the body
C. Neither raises nor lowers the CG of the body
D. None of above
Answer : A

33. On a ladder resting on a rough ground and leaning against a smooth vertical wall, the force of friction acts
A. Downwards at its upper end
B. Upwards at its upper end
C. Perpendicular to the wall at its upper end
D. Zero at its upper end
Answer : D

34. A marble ball is rolled on a smooth floor of a room to hit a wall. If the time taken by the ball in returning to the point of projection is twice the time taken in reaching the wall, the coefficient of restitution between the ball and the wall, is
A. 0.25
B. 0.50
C. 0.75
D. 1.0
Answer : B

35. 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

36. For a simple pendulum, the period of one oscillation is
A. 2? ?(l/2g)
B. 2? ?(2g/l)
C. 2? ?(l/g)
D. 2? ?(g/2l)
Answer : C

37. 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

38. If two equal forces of magnitude P act at an angle ?, their resultant, will be
A. P cos ?/2
B. 2P sin ?/2
C. P tan ?/2
D. 2P cos ?/2
Answer : D

39. The pole distance is measured in
A. Distance scale
B. Force scale
C. Mass scale
D. Time scale
Answer : B

40. A body of weight w placed on an inclined plane is acted upon by a force P parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is ? and angle of friction is ?, the minimum value of P, is
A. w sin (? - ?)/cos ?
B. w sin (? - ?)/cos ?
C. w cos (? + ?)/cos ?
D. w sin? cos(? - ?)/sin ?
Answer : B

41. If te tension in a cable supporting a lift moving upwards is twice the tension when the lift is moving downwards, the acceleration of the lift, is
A. g/2
B. g/3
C. g/4
D. g/5
Answer : B

42. 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

43. 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

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

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. 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

47. A system of coplanar forces is in equilibrium when
A. Force polygon closes
B. Funicular polygon closes
C. Both force polygon and funicular polygon close
D. All the forces are concurrent
Answer : C

48. If ? is the angular acceleration of a compound pendulum whose angular displacement is ?, the frequency of the motion is
A. 2? ?(?/?)
B. (1/2?) ?(?/?)
C. 4? ?(?/?)
D. 2? ?(? - ?)
Answer : B

49. A particle moves with a velocity of 2 m/sec in a straight line with a negative acceleration of 0.1 m/sec2. Time required to traverse a distance of 1.5 m, is
A. 40 sec
B. 30 sec
C. 20 sec
D. 15 sec
Answer : C

50. 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