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Posted By: India Member Level: Diamond Posted Date: 19 Jan 2008
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2007 Jawaharlal Nehru Technological University B.Tech I Year Engineering Mechanics (RR-Set 3 - Aug / Sep'2007- Sup) Question paper
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Code No: RR10302 Set No. 3
I B.Tech Supplimentary Examinations, Aug/Sep 2007
ENGINEERING MECHANICS
( Common to Mechanical Engineering, Mechatronics, Metallurgy &
Material Technology, Production Engineering, Aeronautical Engineering
and Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. Determine the resultant of the four forces and one couple that act on the plate
shown in Figure 1. [16]
Figure 1
2. The two 50 wedges shown in Figure2 are used to adjust the position of the column
under a vertical load of 5 kN. Determine the magnitude of the forces P required to
raise the column if the coefficient of friction for all surfaces is 0.40. [16]
Figure 2
3. An open flat belt drive connects two parallel shafts 1200mm apart. The driving
and driven shafts rotate at 350 r.p.m and 140 r.p.m respectively and the driven
pulley is 400 mm in diameter. The belt is 5mm thick and 80mm wide. Coefficient
of friction between belt and pulley is 0.3 and maximum permissible tension in the
belting is 1.4N/mm2. Determine.
(a) Diameter of driving pulley.
(b) Maximum power that may be transmitted by the belting and
(c) Required initial tension in the belt. Neglect centrifugal tension. [16]
4. (a) From the first principles determine product of inertia for right angle triangle
of base ‘ b’ and altitude ‘ h’.
(b) State and prove transfer formula for product of inertia. [8+8]
5. (a) Prove that the mass moment of inertia of a right circular cone of base radius
‘R’ and height ‘h’, with respect to a diameter of the base is M(3R2 +2h2)/20
where M is the mass of the cone.
(b) Calculate the mass moment of inertia of a circular cone of base radius 300mm
and height 600mm about a line which passes through the mass centre of the
cone and which is parallel to the base of the cone. The mass density of the
cone is 2500 kg/m3. [8+8]
6. (a) An airplane is flying horizontally with a velocity of 450 km/hr at an altitude
of 1960 m towards a target on the ground which is to be bombed. Estimate
where the bomb must be released in order to hit the target and the time of
travel of the bomb. What is the velocity with which the bomb will hit the
target? Also find the angle made by the line of sight of the pilot when the
bomb is released.
(b) The acceleration of a particle is defined by the relation a =kt-4. Knowing that
v=4m/s when t=2sec and v= 1m/s when t=1 sec, determine the constant ‘k’.
Write the equations of motion when x=0 at t=3secs. [8+8]
7. (a) A homogeneous solid cylinder of weight 100 N whose axis is horizontal rotates
about its axis, in frictionless bearings under the action of the weight of a 10N
block which is carried by a rope wrapped around the cylinder. What will be
angular velocity of cylinder two seconds after the motion starts? Assume the
diameter of cylinder as 100cm.
(b) A block of mass 5Kg resting on a 300 inclined plane is released. The block after
travelling a distance of 0.5m along the inclined plane hits a spring of stiffness
15N/cm. Find the maximum compression of spring. Assume coefficient of
friction between the block and the inclined plane is 0.2. As shown in the
Figure 7b. [8+8]
Figure 7b
8. A pendulum having a time period of 1 sec. is installed in a lift. Determine its time
period when
(a) the lift is moving upwards with an acceleration of g
10 .
(b) the lift is moving downwards with an acceleration of g
20 . [16]
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