GATE ME topic:mechanics PYQs & Answers — Page 48

Questions 471–480 of 1040. Imported answers require independent review unless marked reviewed.

A right solid circular cone standing on its base on a horizontal surface is of height

and base radius

. The cone is made of a material with specific weight

and elastic modulus

. The vertical deflection at the mid-height of the cone due to self-weight is given by

Your answerChoose one option.

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A plane frame

(fixed at

and free at

) is shown in the figure. Both members (

and

) have length,

, and flexural rigidity,

. Neglecting the effect of axial stress and transverse shear, the horizontal deflection at free end,

, is

Diagram for Mechanical Engineering question 31

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A tapet valve mechanism in an IC engine comprises a rocker arm ABC that is hinged at B as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge B. The mass moment of inertia of the rocker about B is

kg.m

. The rocker arm dimensions are

cm and

cm. A pushrod pushes the rocker at location A, when moved vertically by a cam that rotates at

rpm. The pushrod is assumed massless and has a stiffness of 15 N/mm. At the other end C, the rocker pushes a valve against a spring of stiffness 10 N/mm. The valve is assumed massless and rigid.

Diagram for Mechanical Engineering question 32

Resonance in the rocker system occurs when the cam shaft runs at a speed of ______ rpm (round off to the nearest integer).

Your answerChoose one option.

496

4739

790

2369

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A power transmission mechanism consists of a belt drive and a gear train as shown in the figure.

Diameters of pulleys of belt drive and number of teeth (

) on the gears 2 to 7 are indicated in the figure. The speed and direction of rotation of gear 7, respectively, are

Your answerChoose one option.

25.68 rpm; clockwise

25.68 rpm; anticlockwise

575.28 rpm; clockwise

575.28 rpm; anticlockwise

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Customers arrive at a shop according to the Poisson distribution with a mean of 10 customers/hour. The manager notes that no customer arrives for the first 3 minutes after the shop opens. The probability that a customer arrives within the next 3 minutes is

Your answerChoose one option.

0.39

0.86

0.50

0.61

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A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness (

) and damper (damping factor,

) in parallel. The designer has the following four isolators:

kN/m,

Arrange the isolators in the ascending order of the force transmitted to the foundation.

Your answerChoose one option.

1-3-4-2

1-3-2-4

4-3-1-2

3-1-2-4

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Let

be a continuous function defined on

. The point

at which the tangent of

becomes parallel to the straight line joining

and

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Consider the system shown in the figure. A rope goes over a pulley. A mass,

, is hanging from the rope. A spring of stiffness,

, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope.

Diagram for Mechanical Engineering question 34

The pulley radius is

and its mass moment of inertia is

. Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is

Your answerChoose one option.

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Activities A, B, C and D for the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are independent of each other.

Activity	A	B	C	D
Mean (days)	6	11	8	15
Variance (days )	4	9	4	9

The probability that the project will be completed within 40 days is ______ (round off to two decimal places).

(Note: Probability is a number between 0 and 1).

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Find the positive real root of

using Newton-Raphson method. If the starting guess (

) is 2, the numerical value of the root after two iterations (

) is ______ (round off to two decimal places).

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GATE ME topic:mechanics PYQs

Question 31

Question 31

Question 32

Question 32

Question 33

Question 33

Question 34

Question 34

Question 35

Question 35