### Multiple Choice Questions and Answers (MCQs) on Theory of Machines

01. The motion between a pair which takes place in __________ is known as incompletely constrained motion.

(A) One direction only
(B) Two directions only
(C) More than one direction
(D) None of these

02. A torsional system with discs of moment of inertia I₁ and I₂ as shown in the below figure, is gear driven such that the ratio of speed of shaft B to shaft A is ‘G’. Neglecting the inertia of gears, the equivalent inertia of disc on shaft B at the speed of shaft A is equal to (A) G.I₂
(B) G².I₂
(C) I₂/G
(D) I₂/G²

03. The frictional torque transmitted in a flat pivot bearing, considering uniform pressure, is (where μ = Coefficient of friction, W = Load over the bearing, and R = Radius of bearing surface)

(A) (1/2) μ W R
(B) (2/3) μ W R
(C) (3/4) μ W R
(D) μ W R

04. A typewriter mechanism has 7 numbers of binary joints, six links and none of higher pairs. The mechanism is

(A) Kinematically sound
(B) Not sound
(C) Soundness would depend upon which link is kept fixed
(D) Data is not sufficient to determine same

05. The magnitude of velocities of the points on a rigid link is

(A) Directly proportional to the distance from the points to the instantaneous centre and is parallel to the line joining the point to the instantaneous centre
(B) Directly proportional to the distance from the points to the instantaneous centre and is perpendicular to the line joining the point to the instantaneous centre
(C) Inversely proportional to the distance from the points to the instantaneous centre and is parallel to the line joining the point to the instantaneous centre
(D) Inversely proportional to the distance from the points to the instantaneous centre and is perpendicular to the line joining the point to the instantaneous centre

06. The maximum efficiency of spiral gears is (where θ = Shaft angle, and φ = Friction angle) (A) sin (θ + φ) + 1/ cos (θ – φ) + 1 (B) cos (θ – φ) + 1/ sin (θ + φ) + 1 (C) cos (θ + φ) + 1/ cos (θ – φ) + 1 (D) cos (θ – φ) + 1/ cos (θ + φ) + 1 Answer: Option C 07. If the opposite links of a four bar linkage are equal, the links will always form a

(A) Triangle
(B) Rectangle
(C) Parallelogram
(D) Pentagon

08. The velocity of a flat-faced follower when it has contact with the flank of a circular arc cam, is given by

(A) ωR cosθ
(B) ω(R – r₁) cosθ
(C) ω(R – r₁) sinθ
(D) ωr₁ sinθ

09. Two systems shall be dynamically equivalent when

(A) The mass of two are same
(B) C.G. of two coincides
(C) M.I. of two about an axis through e.g. is equal
(D) All of the above

10. The motion of a shaft in a circular hole is an example of

(A) Completely constrained motion
(B) Incompletely constrained motion
(C) Successfully constrained motion
(D) None of these

11. A rotary internal combustion engine has __________ cylinders.

(A) Four
(B) Five
(C) Six
(D) Seven

12. Cam size depends upon

(A) Base circle
(B) Pitch circle
(C) Prime circle
(D) Outer circle

13. A point B on a rigid link AB moves with respect to A with angular velocity ω rad/s. The total acceleration of B with respect to A will be equal to

(A) Vector sum of radial component and coriolis component
(B) Vector sum of tangential component and coriolis component
(C) Vector sum of radial component and tangential component
(D) Vector difference of radial component and tangential component

14. The equation of motion for a vibrating system with viscous damping is (d²x/dt²) + (c/m).(dx/dt) + (s/m).x = 0, if the roots of the equation are __________ then the system will be under damped.

(A) Equal
(B) Real
(C) Complex conjugate
(D) None of these

15. The purpose of a link is to

(A) Transmit motion
(C) Act as a support
(D) All of the above

16. The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

(A) m.ω².r sinθ
(B) m.ω².r cosθ
(C) m.ω².r (sin 2θ/n)
(D) m.ω².r (cos 2θ/n)

17. The steering of a ship means

(A) Movement of a complete ship up and down in vertical plane about transverse axis (B) Turning of a complete ship in a curve towards right or left, while it moves forward (C) Rolling of a complete ship sideways
(D) None of the above

18. The height of a Watt’s governor is

(A) Directly proportional to speed
(B) Directly proportional to (speed)²
(C) Inversely proportional to speed
(D) Inversely proportional to (speed)²

19. In a differential band brake as shown in the below figure, if the length OB is greater than OA, then the force P at C should act in the downward direction. (A) Yes
(B) No
(C) Unpredictable
(D) None of these

20. A slider crank chain consists of following numbers of turning and sliding pairs

(A) 1, 3
(B) 2, 2
(C) 3, 1
(D) 4, 0

21. Kinematic pairs are those which have

(A) Point or line contact between the two elements when in motion
(B) Surface contact between the two elements when in motion
(C) Elements of pairs not held together mechanically
(D) Two elements that permit relative motion

22. The displacement of the reciprocating roller follower, when it has contact with the straight flanks of the tangent cam, is given by (where r₁ = Minimum radius of the cam, r₂ = Radius of the roller follower, and θ = Angle turned by the cam from the beginning of the follower displacement)

(A) (r₁ – r₂) (1 – cosθ)
(B) (r₁ + r₂) (1 + cosθ)
(C) (r₁ – r₂) [(1 – cosθ)/cos θ]
(D) (r₁ + r₂) [(1 – cosθ)/cos θ]

23. Longitudinal vibrations are said to occur when the particles of a body moves

(A) Perpendicular to its axis
(B) Parallel to its axis
(C) In a circle about its axis
(D) None of these

24. When brakes are applied to all the four wheels of a moving car, the distance travelled by the car before it is brought to rest, will be

(A) Maximum
(B) Minimum
(C) Zero
(D) None of these