# WBUT Question Papers Cs Mechanical Science

# B Tech Ist Sem Dec 2006

Time : 3 Hours ]

[ Full Marks : 70

Group – A ( Multiple Choice Questions)

- Choose the correct answer from the given alternatives in each of the following questions :

a) Centre of gravity of a solid cone lies on the axis at the height,

. i) one-fourth of the total height above base

ii) one-third of the total height above base

HQ one-half of the total height above base

lv) three-eighth of the total height above base

v) none of these.

b) In the equation of virtual work, which of the following forces is ( are ) neglected ?

i) Reaction of any, smooth surface with which the body is in contact

ii) Reaction of a rough surface of a body which rolls on it without slipping

ill) Reaction at a point or an axis, fixed in space, around which a body is constrained to turn

, iv) All of these

v) None of these. _____

c) M.I. of rectangular area of base b and height d about z-axis is given by

i) bd^{3} / 3

ii) bd^{3}/ 4 ill) bd^{3}/ 6

iv) bd^{3} / 12

v) bd^{3} / 8. I

\

d) M.I. of circular area whose diameter is d about an axis perpendicular to the area passing through its centre is given by

5

A body is resting on a plane inclined at an angle of 30° to horizontal. What force would be required to slide it down, if the co-efficient of friction between body

On a plane resultant stress is inclined at an angle of 30° to the plane. If the normal stress on the plane is 50 N/mm ^{2}, the shear stress on the plane will

b

Equation of motion of a particle is s = 2f^{3} – t^{2} – 2, where s is displacement in metres and t is time in seconds. Acceleration of the particle after 1 second will

The ratio of lateral strain to the linear strain within elastic limit is known as

1) Young’s modulus ii) Bulk modulus

111) Modulus of elasticity • iv) Polsson’s ratio.

Group – B ( Short Answer Questions )

Answer any three questions.

A ball is dropped onto a fixed horizontal surface from height h_{Q}. The co-efficient of

restitution is e. Show that the total vertical distance D. travelled by the ball before it comes to rest is

6

- A bullet of mass m, moving with a horizontal velocity v, hits a stationary block of M. suspended by a massless string of length L. The bullet gets embedded in the block after impact and the two together swings up. Show that the maximum angle of swing ( Le. angle made by the string with the vertical) is

o _ -1 f , M^{2} v^{2} )

^{COS} { 2gL ( M + m) ^{2} j

- State and prove Varignon’s theorem. What is meant by a free-body diagram ?
- With a neat sketch, explain stress-strain diagram for a ductile material.
- What is D’Alembert’s principle ? What is the advantage of using the principle ? How does it differ from Newton’s second law of motion ?

Group – C ( Long Answer Questions )

Answer any three questions. 3 x 15 = 45

- a) Determine the axial moment of inertia of the T-section shown in Fig. 1 about the
- centroidal axis parallel to base. 7

Fig. 1

b) A steel tube 4-5 cm external diameter and 3 mm thick encloses centrally a solid copper bar of 3 cm dia. The bar and the tube are rigidly connected together at the ends at a temperature of 30°C. Find the stress In each metal when heated to 180°C. Also find the increase in length if original length of assembly is 30 cm. Given, a _{8t} = 108 x 10″ ^{5} per °C, a _{copper} = 1-7 x 10” ^{5} per °C,

^{E}»t_{ee}i = ^{2}–^{lx} 10-^{6} kg/cm^{2}. E_{copper}= Mx 10-^{6}kg/cm^{2}. 8

fSEM-1 /ME-101/06

A ball of weight W rests upon a smooth horizontal plane and has attached to its centre two strings AB and AC which pass over frictionless pulleys at B and C and carry loads P and Q respectively, as shown in Fig. 2. If the string AB is horizontal, find the angle a that the string AC makes with the horizontal when the ball is in a position of equilibrium. Also find the pressure R between the ball and the plane. 8

b) Find the acceleration of a falling weight P hanging over a pulley by a string connecting a block Q as shown in the Fig. 3, the co-efficient of friction between block Q and the horizontal plane if slides is p. Neglect inertia of the pulley and friction on its axle. Given, P = 10 kgf, 0=12 kgf, p = + .

: Fig. 3

- a) Determine the maximum ratio h/b for which the homogeneous block will slide without tipping under the action of force P as shown In the Fig. 4. The co-efficient of static friction between the block and the Incline is p .

b) Two blocks of weight W j and W _{2} are located on two inclined planes as

in Fig. 5. Assuming the contact surfaces to be frlctionless, W _{l} = 200 N. W_{2} = 300 N, determine the angle 0 for equilibrium. 7

- a) To anticipate the dip and hump in the road, the driver of a car applies his brakes to produce a uniform deceleration, his speed is 100 km/hr at the bottom A of the dip and 50 km/hr at the top C of the hump, which is 120 m along the road from A. If the passengers experience a total acceleration of 3 m/s
^{2}at A and if the radius of curvature of the hump at C is 150 m. calculate

I) the radius of curvature p at A •

II) the acceleration at the inflexion point B, and

Hi) the total acceleration at C.

b) A broad Jumper approaches his take-off board A with a horizontal velo<*m/s. Determine the vertical component v_{y} of the velocity of his centre of

gravity at take-off for him to make the Jump shown in Fig. 7. What Is the vertical rise h of his centre of gravity ? _{
}

- Two equal uniform rods AC and CB are freely jointed at C and rest In a vertical plane with the ends A and B In contact with a rough horizontal plane. If the equilibrium be limiting and p is the co-efficient of friction, show that

sin Z ACB = – _{0}