# WBUT Question Papers CS Mechanical Science

# B Tech Ist Sem Dec 2007

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

- 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

^{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. ^

^{3}+ 3t

^{2}– 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 )

Answer any three questions. a)

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

H |

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. ®

_{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, = W

_{2}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

- 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

X

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

- 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 ?