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GATE ME THeory of Machines & Vibration : National Champion Test

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Question 1

A slider crank mechanism with crank radius 200 mm and connecting rod length 800 mm is shown. The crank is rotating at 600 rpm in the counter clockwise direction. In the configuration shown, the crank makes an angle of 90 ° with the sliding direction of the slider, and a force of 5 kN is acting on the slider. Neglecting the inertia forces, the turning moment on the crank (in kN-m) is __________

Question 2

General plane motion is:

Question 3

The number of degrees of freedom in a planer mechanism having n links and j simple hinge joints is

Question 4

A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car. The combined moment of inertia of the rotating masses is 10 kg-m2. The magnitude of the gyroscopic moment (in N-m) is __________

Question 5

In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The number of teeth on gear 2, 3, and 4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4 rotates with an angular velocity of 100 rpm in the counter clockwise direction, the angular speed of arm 5 (in rpm) is

Question 6

A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of

the ratio of the amplitude of steady state response to the static deflection of the spring is____

Question 7

A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm.

Question 8

A solid disc with radius a is connected to a spring at a point d above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is M and the spring constant is K. The polar moment of inertia for the disc about its centre is J = Ma²/2.

The natural frequency of this system in rad/s is given by

Question 9

A 4-bar mechanism with all revolute pairs has link lengths $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-2_files\image046.png$ in $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-2_files\image047.png$ , $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-2_files\image048.png$ and $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-2_files\image049.png$ . The suffixes $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-2_files\image050.png$ , ‘in’, 'co’ and ‘out’ denote the fixed link, the input link, the coupler and output link respectively. Which one of the following statements is true about the input and output links?

Question 10

Which of the following is a lower pair __________?

Question 11

A gear train is made up of five spur gears as shown in the figure. Gear 2 is driver and gear 6 is driven member. N₂. N₃, N₄. N₅ and N₆ represent number of teeth on gears 2, 3, 4, 5, and 6 respectively. The gear(s) which act(s) as idler(s) is/are

Question 12

Which relation is suitable among Gear 1 and gear 4 in terms of angular velocity?

Question 13

Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the figures. The moment of inertia (in kg.m²) of the flywheel is

Question 14

In the figure shown, the relative velocity of link 1 with respect to link 2 is 12 m/sec. Link 2 rotates at a constant speed of 120 rpm. The magnitude of Coriolis component of acceleration of link 1 is
$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE ME 18-Mar\GATE-ME-2004_files\image140.jpg$

Question 15

Match the approaches given below to perform stated kinematics/dynamics analysis of machine.

Question 16

In a four-bar linkage, S denotes the shortest link length, L is the longest link length, P and Q are the lengths of other two links. At least one of the three moving links will rotate by 360 ° if

Question 17

Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is (r=1 m)

Question 18

A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its centre and laterally supported at one end by a spring of spring constant k = 300 N/m. The natural frequency ω_n in rad/s is

Question 19

The figure below shows a planar mechanism with single degree of freedom. The instantaneous centre 24 for the given configuration is located at a position
$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE ME 18-Mar\GATE-ME-2004_files\image142.png$

Question 20

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-2_files\image135.png$ and $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-2_files\image136.png$ as shown below.

$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-ME-2014-Set-2_files\image137.png$

Question 21

A single cylinder, four- stroke IC engine rotating at 900 rpm has crank length of 50 mm and a connecting rod length of 200 mm. If the effective reciprocating mass of the engine is 1.2 kg, what is the approximate magnitude of the maximum shaking force’ created by the engine

Question 22

The number of instantaneous centres of rotation for a 10 link kinematic chain is

Question 23

As compared to the time period of a simple pendulum on the earth, its time period on the moon will be

Question 24

which one of the following is the correct value of the natural frequency

of the system given below?

Question 25

When a rotor of mass 100 kg is mounted on a shaft, a bending deflection of 0.1 mm is observed at the place where the rotor is placed, what is the dangerous speed(rpm) of the rotor?