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CHAPTER 4 THEORY OF MACHINES YEAR 2012 MCQ 4.1 ONE MARK The following are the data for two crossed helical gears used for speed reduction : Gear I : Pitch circle diameter in the plane of rotation 80 mm and helix angle 30c. Gear II : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5c. If the input speed is 1440 rpm, the output speed in rpm is (A) 1200 (B) 900 (C) 875 MCQ 4.2 A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity ω and angular acceleration α. The magnitude of the acceleration of the point of contact on the disc is (A) zero (B) rα (C) MCQ 4.3 MCQ 4.4 (D) 720 (rα) 2 + (rω2) 2 (D) rω 2 In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is (Note. All dimensions are in mm). (A) 0.05 (B) 0.1 (C) 5.0 (D) 10.0 A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is GATE Previous Year Solved Paper For Mechanical Engineering Published by: NODIA and COMPANY Visit us at: www.nodia.co.in ISBN: 9788192276250

www.gatehelp.com PAGE 156 THEORY OF MACHINES CHAP 4 (A) 395 (B) 790 (C) 1580 (D) 3160 YEAR 2012 MCQ 4.5 TWO MARKS A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k . For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is (A) k m (B) 2k m (C) k 2m (D) 4k m YEAR 2011 MCQ 4.6 ONE MARK A double-parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is (A) − 1 (B) 0 (C) 1 (D) 2 YEAR 2011 MCQ 4.7 TWO MARKS For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. The length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD in rad/s is GATE Previous Year Solved Paper For Mechanical Engineering Published by: NODIA and COMPANY Visit us at: www.nodia.co.in ISBN: 9788192276250

www.gatehelp.com CHAP 4 MCQ 4.8 MCQ 4.9 THEORY OF MACHINES PAGE 157 (A) 3 (B) 3 2 (C) 1 (D) 2 3 A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the figure. Under the frictionless conditions, the natural frequency of the system in Hz is close to (A) 32 (B) 23 (C) 16 (D) 11 A disc of mass m is attached to a spring of stiffness k as shown in the figure The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is (A) 1 2π k m (B) 1 2π 2k m (C) 1 2π 2k 3m (D) 1 2π 3k 2m YEAR 2010 MCQ 4.10 ONE MARK Mobility of a statically indeterminate structure is GATE Previous Year Solved Paper For Mechanical Engineering Published by: NODIA and COMPANY Visit us at: www.nodia.co.in ISBN: 9788192276250

www.gatehelp.com PAGE 158 MCQ 4.11 THEORY OF MACHINES CHAP 4 (A) #− 1 (B) 0 (C) 1 (D) $ 2 There are two points P and Q on a planar rigid body. The relative velocity between the two points (A) should always be along PQ (B) can be oriented along any direction (C) should always be perpendicular to PQ (D) should be along QP when the body undergoes pure translation MCQ 4.12 Which of the following statements is INCORRECT ? (A) Grashof’s rule states that for a planar crank-rocker four bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths (B) Inversions of a mechanism are created by fixing different links one at a time (C) Geneva mechanism is an intermittent motion device (D) Gruebler’s criterion assumes mobility of a planar mechanism to be one MCQ 4.13 The natural frequency of a spring-mass system on earth is ωn . The natural frequency of this system on the moon (g moon = g earth /6) is (A) ωn (B) 0.408ωn (C) 0.204ωn (D) 0.167ωn MCQ 4.14 Tooth interference in an external involute spur gear pair can be reduced by (A) decreasing center distance between gear pair (B) decreasing module (C) decreasing pressure angle (D) increasing number of gear teeth YEAR 2010 MCQ 4.15 TWO MARKS A mass m attached to a spring is subjected to a harmonic force as shown in figure The amplitude of the forced motion is observed to be 50 mm. The value of m (in kg) is GATE Previous Year Solved Paper For Mechanical Engineering Published by: NODIA and COMPANY Visit us at: www.nodia.co.in ISBN: 9788192276250

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