# WBUT Question Papers CS Mechanical Science

# B Tech Ist Sem Dec 2009 10

- The figures in the margin indicate full marks.
- Candidates are required to give their answers in their own words
- as far as practicable. GROUP – A ( Multiple Choice Type Questions )

- Choose the correct alternatives of the following : 10 x 1 = 10

i) Lami’s theorem is applicable to

^{2}cos

^{2}a/2g b) u

^{2}sin

^{2}a/2g c) u

^{2}tan

^{2}a/2g d) u

^{2}sin

^{2}a/g. x) Three forces V3p, p and 2p acting on a particle are in equilibrium. If the angle between first and second be 90°, the angle between second and third will be a) 30°

GROUP -B ( Short Answer Type Questions )

Answer any three of the following. 3×5= 15

- a) State D’ Alembert’s principles.

b) A smooth circular cylinder of radius 1-5 is lying in a rectangular groove is shown in Figure 1. Find the reactions at the surfaces of contact, if there is no friction and the cylinder weighs 1000 N. 1+4

- Refer to the Figure 2, determine the range of values of mass m
_{0}so that the 100 kg block will neither move up nor slip down the inclined plane. The coefficient of static friction for the surfaces in contact is 0-3.

- a) State Varigon’s principle.

b) A circular roller of weight 100 N and radius 10 cm hangs by a ties rod AB = 20 cm and rests against a smooth vertical wall at C as shown in Figure 3. Determine the force F in the rod.

- Referring to Figure 4, r = 12 cm, Q = 500 N and h = 6 cm. Find magnitude of P required to start the roller over curb.

- Two smooth circular cylinders of Figure 5, each of weight W = 100 N and radius r = 6 cm are connected by a string AB of length I = 16 cm and rest upon a horizontal plane, supporting a third cylinder of weight Q = 200 N and radius r = 6 cm above them. Find the tension S in the string AB and the pressure produced by the floor at points of contact D and E.

Q
n vr Figure 5 |

GROUP -C ( Long Answer Type Questions )

Answer any three of the following. 3 x 15 = 45

- a) A 150 kg man stands on the mid-point of a 50 kg ladder

as shown in Figure 6. Assuming that floor and the wall are perfectly smooth, find the reactions at points A and B.

b) Determine the moment of inertia for the T section ( as shown in Figure 7 ) with respect to a centroidal axis parallel to x-axis. All dimensions are in mm. 8 + 7

- a) Prove that the volumetric strain of a rectangular bar is the algebraic sum of strains of length, width and height.

b) Show that elongation of a conical bar under its own weight is independent of its base diameter but on length only.

6 + 4 + 5

- a) Two spheres P and Q rests in the channel as shown in Figure 8. The sphere P has a diameter 400 mm and weight of 200 N, whereas the sphere Q has diameter 500 mm and weight 500 N. If bottom width of the channel is 500 mm and with one side vertical and other side inclined at 60°, determine the reaction induced in the contacts.

b) In the Figure 9 shown, find the minimum value of horizontal force P applied to the lower block that will keep the system in equilibrium. Given, coefficients of friction between lower block and floor = 0-25, between the upper block and the vertical wall = 0-30, between the two blocks = 0-20. 8 + 7

- a) State the principle of virtual work. 3

b) Two blocks weighing W, and W_{2} resting on smooth inclined planes are connected by an inextensible string passing over a smooth pulley as shown in Figure 10. Find the value of W_{2} when W_{l} = 500 N and a = 30°, p = 60°. 7

) Determine velocity V of the falling weight W of the system as shown in Figure 11 as a function of its displacement from the initial position of rest. Assume weight of the cylinder as 2W.

Figure 11

- a) From top of a tower. 60 m high a bullet is fired at an angle of 20° up the horizontal with velocity 120 m/s. Determine

i) time of flight ii) horizontal range of ground

iii) maximum height of the bullet from ground

iv) velocity of the bullet after 8 seconds. Assume horizontal ground at the foot of the tower. b) Determine the tension in the strings and accelerations of two blocks of masses 150 kg and 50 kg connected by a string and a frictionless, weightless pulley as shown in Figure 12. 10 + 5