SSC Stenographer - Applied Mechanics and Graphic Statics 1000+ MCQ [Solved] PDF Download

1. 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

2. The motion of a particle moving with S.H.M. from an extremity to the other, constitutes
A. Half an oscillation
B. One full oscillation
C. Two oscillations
D. None of these
Answer : A

3. In a simple harmonic motion, the position of equilibrium is always
A. Stable
B. Unstable
C. Neutral
D. None of the above
Answer : A

4. The reaction at the central support B of the beam ABC hinged at D shown in below figure is
A. 2 t
B. 5.8 t
C. 0.2 t
D. 3.5 t
Answer : B

5. A Second's pendulum gains 2 minutes a day. To make it to keep correct time its length
A. Must be decreased
B. Must be increased
C. Is not changed but weight of the bob is increased
D. Is not changed but weight of the bob is decreased
Answer : B

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

7. A number of forces acting simultaneously on a particle of a body
A. May not be replaced by a single force
B. May be replaced by a single force
C. May be replaced by a single force through C.G. of the body
D. May be replaced by a couple
Answer : B

8. One end of a light string 4 m in length is fixed to a point on a smooth wall and the other end fastened to a point on the surface of a smooth sphere of diameter 2.25 m and of weight 100 kg. The tension in the string is
A. 17.5 kg
B. 19.5 kg
C. 22.5 kg
D. 25 kg
Answer : C

9. 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

10. 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

11. 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

12. In the structure shown in below figure, the member which carries zero force, is
A. AB
B. BC
C. BE
D. All the above
Answer : D

13. The necessary condition of equilibrium of a body is:
A. Algebraic sum of horizontal components of all the forces must be zero
B. Algebraic sum of vertical components of all the forces must be zero
C. Algebraic sum of the moments of the forces about a point must be zero
D. All (a), (b) and (c)
Answer : D

14. 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

15. If the resultant of two forces P and Q acting at an angle ? makes an angle ? with P, then tan ? equals
A. P sin ?/P - Q cos ?
B. Q sin ?/P + Q cos ?
C. P sin ?/P + Q tan ?
D. Q sin ?/P + Q sin ?
Answer : B

16. Total no of instantaneous centres of a machine having n links, is
A. n/2
B. n
C. (n - 1)
D. n (n - 1)/2
Answer : D

17. 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

18. The C.G. of the shaded area of the below figure whose curve OM is a parabola from y-axis, is
A. a/4
B. 3a/4
C. 3b/10
D. 3a/10
Answer : B

19. 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 re
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

20. 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

21. 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

22. Pick up the incorrect statement from the following. In a simple 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

23. 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

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

25. Joule is the unit of
A. Work
B. Force
C. Power
D. Torque
Answer : A

26. 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

27. If two forces each equal to T in magnitude act at right angles, their effect may be neutralised by a third force acting along their bisector in opposite direction whose magnitude will be
A. 2 T
B. 1/2 T
C. ?2 T
D. 3 T
Answer : C

28. 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

29. 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

30. According to Law of Triangle of Forces
A. Three forces acting at a point, can be rep-resented by the sides of a triangle, each side being in proportion to the force
B. Three forces acting along the sides of a triangle are always in equilibrium
C. If three forces acting on a, point can be represented in magnitude and direction, by the sides of a triangle taken in order, these will be in equilibrium
D. If the forces acting on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant will be represented in magnitude and direction by the third side of the triangle, taken in opposite order
Answer : D

31. 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

32. Rate of change of angular momentum is equal to
A. Force
B. Torque
C. Linear momentum
D. Impulse
Answer : B

33. 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

34. The bending moment in an arch is proportional to
A. Vertical ordinate of funicular polygon
B. Vertical ordinate of the arch
C. Intercept between the arch axis and the funicular polygon
D. None of these
Answer : C

35. 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

36. 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

37. 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

38. Instantaneous center is at infinity when the angular velocity is
A. Constant
B. Zero
C. Maximum
D. Minimum
Answer : B

39. The angular speed of a car while taking a circular turn of radius 100 m at 36 km/hour, is
A. 0.1 radian/sec
B. 1 radian/sec br>C. 100 radian/sec
D. 1000 radian/sec
Answer : A

40. 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

41. 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

42. 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

43. A satellite is said to move in a synchronous orbit if it moves at an altitude of 36, 000 km with a maximum velocity of about
A. 7000 km per hour
B. 8000 km per hour
C. 9000 km per hour
D. 11,000 km per hour
Answer : @

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

45. Pick up the correct statement from the following:
A. Nature plays an important role in the launch of a satellite
B. The earth's gravity reduces the speed of a satellite by 32 km per second
C. The gravitational force relents as the satellite climbs higher
D. All the above
Answer : D

46. 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

47. A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about (Assume g = 10 m/sec²)
A. 1/4
B. 1/3
C. 1/2
D. 1/5
Answer : A

48. A body is dropped from a height of 100 m and at the same time another body is projected vertically upward with a velocity of 10 m/sec. The two particles will
A. Never meet
B. Meet after 1 sec
C. Meet after 5 sec
D. Meet after 10 sec
Answer : D

49. The vertical reaction at the support A of the structure shown in below figure, is
A. 1 t
B. 2 t
C. 3 t
D. 3.5 t
Answer : C

50. 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