# B Tech Ist Sem Dec 2007

[ Full Marks : 70 GROUP-A (Multiple Choice Type Questions)

1. Choose the correct alternatives for the following :                         10×1 = 10

i)          Two non-collinear parallel equal forces in opposite direction a) balance each other     b) constitute a moment

c) constitute a couple    d) constitute a moment of couple

e) constitute a resultant couple. il) The centre of gravity of a uniform lamina lies at a) the centre of heavy portion b) the bottom surface c) the mid-point of its axes  d) all of these e) none of these. ill) The ratio of limiting friction and reaction is known as a) coefficient friction-  b) angle of friction c) angle of repose        d) sliding friction e) friction resistance. tv) D* Alembert’s principle is applied to solve problems related to a) Statics                b) Stress of a structure c) Dynamics               d) none of these. v)         Materials having same elastic properties in all directions are called a) Ideal material         b) Isotropic material c) Elastic material d) Uniform material.

vi)        The energy absorbed in the body when it is strained within the elastic limit is
a)                                                                                  strain energy b) resilience c) toughness              d) modulus of resilienc

A Jet engine works on the principle of conservation of a)                                                                                  energy     b) mass c) angular momentum                   d) linear momentum e) none of these. When a body slides down an inclined surface ( angle of inclination = 0 ), the acceleration /of the body is given by

a)        J=g c)        f = g cos 0 e) / = g / sin 0.

.                       GROUP – B ( Short Answer Type Questions ) Answer any three of the following.                     3×5= 15 State Varignon’s Principle.                                                                        2 Determine the tension in the tie rod AC = 300 mm when a circular roller of weight Q = 450 N and radius r = 150 mm is rest against a vertical wall at B as shown in Fig. 1.  ^

a)          State and prove Laml’s theorem. b)          State the principle of Transmlssibility of forces. Define clearly : a)          Malleability 4 b)          Resilience                                                                   * c)          Toughness and d)          Poisson’s ratio.                                                                                 5 a)          State D’ Alembert principle.                                                              2 b)         The position of a particle is given by, S = 4t3 + 3t2 – 18t + 5, when S is in metre, t in second. Determine the velocity and acceleration at t = 3 seconds. 3 A force given by F = 3i + 2j – 4k is applied at the point P ( 1, – 1, 2 ). Find the moment of the force F about the point O ( 2, – 1, 3 ).                                                ■                          5

GROUP -C ( Long Answer Type Questions )

The tension In the supporting cable AB ( Fig. 2 ) is 10 kN. Write the force which the cable exerts on the boom BC as a vector T. Determine the angle 0 x , 0 and 0 z which the line of action of T forms with the positive x-, y- and z-axes.                               7

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CS/B.TECH/8EM-1/ME’101/07/(OS)                    6 b)         A roller of radius r = 12 cm and weight Q = 5 kN is to be rolled over a curb height h = 6 cm by a horizontal force P applied to the end of a string around the circumference of the roller as shown In Fig. 3. Find the magnitude of P required to start the roller over the curb. There is sufficient friction between the roller surface and the edge of the curb to prevent slip at A.                  8 / Q

Pig. 3 8. a) A slender prismatic bar AB of length I and weight Q stands in a vertical plane and Is supported by smooth surfaces at A and B as shown in Fig. 4. Using the principle of virtual work, find the magnitude of the horizontal force P applied at A if the bar is In equilibrium.                                                                                             7

b)          A projectile is launched with an Initial speed of 200 m/s at an angle of 60° ( Fig. 5 ) with respect to the horizontal. Compute the range R as measured up the Incline.     ®

/ j/.TECH/8EM-1 /ME-101/07/(08)        7                                                      : ■ ■17 ‘ Illl a)         Two rectangular blocks of weights W t and W 2 are connected by a flexible cd>rd and rest upon a horizontal and an inclined plane, respectively, with the cord passing over a pulley as shown in Fig. 6. In the particular case where W, = W2 and the coefficient of static friction p is the same for all contiguous surfaces, then And the angle a of inclination of the inclined plane at which motion of the system will Impend. Neglect friction in the pulley.                                                      10

b)            A particle is moving along a circular path having a radius of 4 m such that its position as a function of time is given by 0 = cos 2t where 6 is In radians and t is in seconds. Determine the magnitude of the velocity of the particle when 6 = 30°.       5

1. a) A slender bar AB of length I which remains always in the same vertical plane has its ends A and B constrained to remain in contact with a horizontal floor and a vertical wall, respectively as shown in Fig. 7. The bar starts from a vertical position and the end A Is moved along the floor with constant velocity u 0 so that its displacement OA = v 0 t. Find the displacement time and acceleration time equations for the vertical motion of the end B of the bar.                                                                                8

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b)         A 20 tonnes goods train is travelling at a constant speed of 100 km/hr while total resistance against the motion due to ground friction and air pressure is 50 N per tonne weight. Suddenly the last wagon weighing 20 tonnes gets decoupled and falls behind the main train. Determine : i)          the acceleration and deceleration of the main train and decoupled wagon respectively

ii)         the distance between the two after 20 seconds.                                 7

1. a) Referring to Fig. 8 determine the coordinates of the centre of the circular hole cut in a thin plate so that this point will be the centre of gravity of the remaining shaded area.                                                                                                        ®

b)
In Fig. 9 a lever is attached to a spindle by means of a square key 6 mm x 6 mm by 2-5 cm long. If the average shear stress in the key not to exceed 700 kg/cm 2 , what is the safe value of the load P applied to the end of the lever ?