Bengal Engineering and Science University 2006 B.E Electrical Engineering Engineering Mechanics and Graphics-IC - Question Paper

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The ques. paper is with the attachment in pdf format.

Bx/BESUS/AM-203/ 06S

B.E. (EE) Part-I 2nd Semester Suppl. Examination, 2006

Engineering Mechanics and Graphics-IC (AM-203)

Time : 3 hours

(For Old A_ul_ati_on)

Ful, Marks

Use separate answerscript _ for each half. Answer SIX questions, taking THREE from each half.

The questions are of equal value. Two marks are reserved for neatness in each half.

FIRST HALF

1. Weights W and 2 W are supported in vertical plane by

a string and pulleys arranged as shown in Fig.Q.l. Find the magnitude of an additional weight Q applied on the left which will give a downward acceleration

0.1 g to the weight W. Neglect inertia and friction of pulleys.

2. Neglecting friction and inertia of the two-step pulleys

shown in Fig.Q.2, find the acceleration of the weight P. Assume P = 36N, Q=54N and r₂ = 2r,.

3. Find the time period for small oscillations of the compound pendulum shown in Fig.3Q. Treat OD and AB as identical slender bars of uniform cross-section.

fp

j^-1

At-

D

B

M4-H

Fig.Q3

4. a) A small car of weight W starts from rest at A and rolls without friction along the loop-the-loop ACBD as shown in Fig.Q.4a. What is the least height '/z' above the top of the loop at which the car can start without falling off the track at point B, and for such a starting position what velocity with the car have along the horizontal portion CD of the track? Neglect friction.

Fig.Q.4a

b) An automobile of weight W travels with uniform speed v over a vertical curve ACB (Fig.Q.4b) which is parabolic. Determine the total pressure R (in terms of v, / & 8) exerted on the road by the four wheels of the car as it passes the crest 'C\

c

A ^Y/ B

^r 1

~4.1

I

" 2

2

Fig.Q.4b

5. At what uniform speed of rotation around the vertical axis AB will the balls C and D of equal weights Wbegin to lift the weight Q of the device shown in Fig.Q.5? The following numerical data are given : W=4.5N, Q = 9.0N,/ = 0.254 m. Neglect all friction and the weights of the four hinged bars of length /. The weight Q can slide freely along the shaft A6.

A

- (3) -SECOND HALF

6. Two spheres each of weight 1000 N and of radius 25 cm rest in a horizontal channel of width 90 cm as shown in Fig.Q.6. Find the reactions on the points of contact

A, B and C.

Fig.Q.6

7. A block of weight W\ = 1000N rests on a horizontal surface and supports on its top another block of weight W_x = 250N as shown in Fig.Q.7. The weight W₂ is attached by an inclined string AB to vertical wall. Find magnitude of horizontal force P applied to lower block to cause slipping to impend. Assume coefficient of friction for all surfaces of contact to be 0.3.

Fig.Q.7

8. Determine the coordinates of the centre of a 4 cm diameter circular hole cut in a thin plate so that this point will be the centroid of the remaining shaded area. Refer Fig.Q.8.