WBUT Exam Papers
Table of Contents
Mechanical Sciences 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) onefourth of the total height above base
ii) onethird of the total height above base
HQ onehalf of the total height above base
lv) threeeighth 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 zaxis is given by
i) bd^{3} / 3
ii) bd^{3}/ 4 ill) bd^{3}/ 6
iv) bd^{3} / 12
v) bd^{3} / 8. I
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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 coefficient of friction between body
and plane is 03 ?  
1)  zero 
11)  1 kg 
.111)  5 kg 
iv)  would depend 
v)  none of these. 
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 be


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 be
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 coefficient of
restitution is e. Show that the total vertical distance D. travelled by the ball before it comes to rest is
( ^{1}^{+<?2}1 I – e^{2} j
 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 freebody diagram ?
 With a neat sketch, explain stressstrain 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.
 a) Determine the axial moment of inertia of the Tsection shown in Fig. 1 about the
 centroidal axis parallel to base.
b) A steel tube 45 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} = 17 x 10” ^{5} per °C,
^{E}»t_{ee}i = ^{2}–^{lx} 10^{6} kg/cm^{2}. E_{copper}= Mx 10^{6}kg/cm^{2}.
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.
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 coefficient 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 = + .
 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 coefficient of static friction between the block and the Incline is p . 8
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.
 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 takeoff board A with a horizontal velo<*tytf ^{10} m/s. Determine the vertical component v_{y} of the velocity of his centre of
gravity at takeoff 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 coefficient of friction, show that
sin Z ACB = – _{0}
1 + 4p ^{2}
8 m/sec^{2} ill) 10 m/sec^{2}