# WBUT Exam Papers

## Time : 3 Hours ]

Full Marks : 70

Group – A ( Multiple Choice Questions)

1. 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)            bd3 / 3

ii)          bd3/ 4 ill) bd3/ 6

iv)         bd3 / 12

v)           bd3 / 8.                                         I

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CS/B.Tech/SEM-1/ME-101/06

 d)
 M.I. of circular area whose diameter is d about an axis perpendicular to the area passing through its centre is given by
 i) ii) iii)
 {R + h) R
 In order to avoid overturning for a vehicle moving on a level curved path, the maximum permissible velocity must be 0 vmax * [ 9ra / M1/2
 f)

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

 and plane is 0-3 ? 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

 i) 43-3 N/mm 2 ill) 100 N/mm2
 -ii) 86 6 N/mm 2 iv) None of these.

Equation of motion of a particle is s = 2f3 – t2 – 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 )

A ball is dropped onto a fixed horizontal surface from height hQ. The co-efficient of

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

( 1+<?21 I – e2 j

1. 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 ,         M2 v2 )

COS { 2gL ( M + m) 2 j

1. State and prove Varignon’s theorem. What is meant by a free-body diagram ?
2. With a neat sketch, explain stress-strain diagram for a ductile material.
3. 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 )

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

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»teei = 2lx 10-6 kg/cm2. Ecopper= Mx 10-6kg/cm2.

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 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 = + .

1. 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 .                                                                         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. W2 = 300 N, determine the angle 0 for equilibrium.

1. 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<*tytf 10 m/s. Determine the vertical component vy 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 ?

1. 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

1  + 4p 2

8 m/sec2 -ill) 10 m/sec2