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GAYATRI VIDYA PARISHAD COLLEGE OF ENGINEERING (AUTONOMOUS)Madhurawada, Visakhapatnam

Affiliated to JNT University K, Kakinada B. Tech. I -Semester Regular Examinations, Dec/Jan 2011-12

Engineering Mechanics (Common to CSE, EEE & IT)

Date : 26/12/2011 Time : 3 Hours Max. Marks : 601. Question No. 1 is Compulsory. 2. Answer any FOUR from questions 2 to 8.3. All parts of a Question must be answered in one place to get valued.

1. Answer the following questions.

a) State the parallelogram law of forces.b) Explain how to resolve a force in space to determine its components.

c) Discuss the various support reactions.d) Define angle of friction, angle of repose and cone of friction.e) Explain why the first moment of an area with an axis of symmetry is zero.f) State the relationship between the area moment of inertia and mass moment of inertia for a

thin uniform plate.g) Express the acceleration of a particle in tangential and normal components.h) The angular motion of a disc is given by the relation . 234 23 t t t += Determine the

angular displacement, velocity and acceleration at time t=2s.

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2. a) State and prove Varignons theorem.b) An equilateral triangular plate of side 3m is acted on by three forces as shown in Figure2(b).

Replace them by an equivalent force-couple system at A.

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3. a) A roller of radius r=12cm and weight Q=500N is to be pulled over a curb of height h=6cmby a horizontal force p applied to the end of a string wound around the circumference ofthe roller (Figure3(a)). Find the magnitude of P required to start the roller over the curb.

b) A sphere of weight W is suspended by a string attached to a vertical wall as shown inFigure3. Determine the inclination of the string if the tension in it is one and a half timesthat of the weight of the sphere. Also determine the reaction between the sphere and thewall.

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4. a) Two blocks of weights W 1 and W 2 rest on a rough inclined plane and are connected by ashort piece of string as shown in figure4(a). If the coefficients of friction are 2.01 = and

3.02 = respectively, find the angle of inclination of the plane for which sliding willimpend. Assume W 1 =W 2 =5N.

b) Derive the expression for effort required to raise the load by using the Screw Jack.

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5. a) Determine the centroid of given shaded portion by using integration method (Figure5(a)).

b) Find the centroid of the shaded area (Figure5(b)).

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6. a) Determine the moment of Inertia of a regular hexagonal section of side a about thehorizontal centroidal axis.

b) Derive the expression for the moment of inertia of a homogeneous right circular cone ofmass m, base radius r and altitude h with respect to its geometric axis.

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7. a) The x and y coordinates of the position of a particle moving in a curvilinear motion aredefined by 232 t x += and 33 t y += . Determine the particles position, velocity andacceleration a .3st =

b) A Pelton wheel turbine used in a lab runs at 1200rpm, when the water jet is suddenly shutoff. If it comes to rest in 30 seconds, determine the retarding torque due to friction inthe bearings assuming it to be uniform. The mass of the wheel is 20kg, and the radiusof gyration is 20cm.

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8. a) A cylinder of mass m and radius r resting on an inclined plane is released from rest androlls down the inclined plane without slipping. Determine the acceleration of its centre ofmass.

b) The system shown in Figure8(b) is released from rest in the configuration shown. Find thevelocity v of the block Q after it falls a distance h=3m. Neglect friction and inertia of thepulleys and assume that P=Q=40N. Use Work - Energy principle.

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