Applied Mechanics and Graphic Statics MCQ Solved Paper for IBPS PO

1. A ladder of weight 'w' rests against a smooth vertical wall, and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being 1/4. The maximum angle of inclination of the ladder to the vertical, if a man of weight 'w' is to walk to the top of it safely, is tan'1 x, where x is
A. 1/4
B. 1/3
C. 3
D. 4
Answer : B

2. The velocity of a moving body, is
A. A vector quantity
B. A scalar quantity
C. A scalar as well as a vector quantity
D. None of these
Answer : A

3. It is observed that in a certain sinusoidal oscillation, the amplitude is linearly dependent on the frequency f. If the maximum velocity during the oscillation is V, then V must be proportional to
A. f
B. 1/f
C. 1/f²
D. f²
Answer : D

4. The motion of a bicycle wheel is
A. Translatory
B. Rotary
C. Rotary and translatory
D. Curvilinear
Answer : C

5. In a lifting machine a weight of 5 kN is lifted through 200 mm by an effort of 0.1 kN moving through 15 m. The mechanical advantage and velocity ratio of the machine are respectively
A. 50 and 75
B. 75 and 50
C. 75 and 75
D. 50 and 50
Answer : A

6. A train weighing 196 tonnes experiences a frictional resistance of 5 11/22 per tonne. The speed of the train at the top of a down gradient 1 in 78.4 is 36 km/hour. The speed of the train after running 1 km down the slope, is
A. 5 ?10 m/sec
B. 10 ?5 m/sec
C. 5 ?3 m/sec
D. 3 ?5 m/sec
Answer : A

7. The C.G. of a right circular cone lies on its axis of symmetry at a height of
A. h/2
B. h/3
C. h/4
D. h/5
Answer : C

8. At the instantaneous center, the velocity of the moving lamina at any instant is
A. Zero
B. Maximum
C. Minimum
D. Varying
Answer : A

9. 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

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

11. 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

12. 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

13. 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
C. 100 radian/sec
D. 1000 radian/sec
Answer : A

14. 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

15. 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

16. If the linear velocity of a point on the rim of a wheel of 10 m diameter, is 50 m/sec, its angular velocity will be
A. 20 rad/sec
B. 15 rad/sec
C. 10 rad/sec
D. 5 rad/sec
Answer : D

17. Two particles have been projected at angles 64° and 45° to the horizontal. If the velocity of projection of first is 10 m/sec, the velocity of projection of the other for equal horizontal ranges is
A. 9.3 m/sec
B. 8.3 m/sec
C. 7.3 m/sec
D. 6.3 m/sec
Answer : A

18. The Law of Polygon of Forces states that
A. If a polygon representing the forces acting at point in a body is closed, the forces are in equilibrium
B. If forces acting on a point can be represented in magnitude and direction by the sides of a polygon taken in order, then the resultant of the forces will be represented in magnitude and direction by the closing side of the polygon
C. If forces acting on a point can be represented of a polygon taken in order, their sides of a polygon taken in order, their resultant will be represented in magnitude and direction by the closing side of the polygon, taken in opposite order
D. If forces acting on a point can be represented in magnitude and direction by the sides of a polygon in order, the forces are in equilibrium
Answer : C

19. 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 bal B just after impact would be
A. Zero
B. 5 m/sec
C. 10 m/sec
D. None of these
Answer : A

20. The moment of inertia of the shaded portion of the area shown in below figure about the X-axis, is

A. 229.34 cm4
B. 329.34 cm4
C. 429.34 cm4
D. 529.34 cm4
Answer : C

21. A string of length 90 cm is fastened to two points A and B at the same level 60 cm apart. A ring weighing 120 g is slided on the string. A horizontal force P is applied to the ring such that it is in equilibrium vertically below B. The value of P is:
A. 40 g
B. 60 g
C. 80 g
D. 100 g
Answer : C

22. 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

23. 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

24. The graphical method of determining the forces in the members of a truss is based on
A. Method of joint
B. Method of section
C. Either method
D. None of the two methods
Answer : A

25. 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

26. 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

27. 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

28. A system of coplanar forces acting on a rigid body can be reduced to
A. One force only
B. One couple only
C. One force and one couple only
D. None of the above
Answer : C

29. Impulse can be obtained from a
A. Force-displacement diagram
B. Force-time diagram
C. Velocity-time diagram
D. Velocity-displacement diagram
Answer : B

30. Varingons theorem of moments states
A. Arithmetical sum of the moments of two forces about any point, is equal to the moments of their resultant about that point
B. Algebraic sum of the moments of two forces about any point, is equal to the moment of their resultant about that point
C. Arithmetical sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
D. Algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
Answer : D

31. Maximum efficiency of a screw jack for the angle of friction ?, is
A. sin ?/(1 + sin ?)
B. (1 - sin ?)/sin ?
C. (1 + sin ?)/(1 - sin ?)
D. (1 - sin ?)/(1 + sin ?)
Answer : D

32. 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 reaction between the sphere and the wall of the arrangement made is
A. 102.5 kg
B. 105.5 kg
C. 108.5 kg
D. 110 kg
Answer : A

33. 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

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

35. The forces which meet at one point and have their lines of action in different planes are called
A. Coplanar non-concurrent forces
B. Non-coplanar concurrent forces
C. Non-coplanar non-current forces
D. Intersecting forces
Answer : B

36. 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

37. A simple pendulum of length l has an energy E, when its amplitude is A. If the length of pendulum is doubled, the energy will be
A. E
B. E/2
C. 2E
D. 4E
Answer : B

39. 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

40. 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 : @

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

42. 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

43. 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

44. 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

45. The angle of friction is:
A. The ratio of the friction and the normal reaction
B. The force of friction when the body is in motion
C. The angle between the normal reaction and the resultant of normal reaction and limiting friction
D. The force of friction at which the body is just about to move
Answer : C

46. 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

47. 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

48. The height at which the end of a rope of length l should be tied so that a man pulling at the other end may have the greatest tendency to overturn the pillar, is
A. ¾ l
B. ½ l
C. l/?2
D. 2/?3 l
Answer : C

49. 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

50. If the 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