JNTU
JNTU B.Tech II ENGINEERING MECHANICS Previous Question Paper (March 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Six forces of magnitudes 20, 30, 40, 50, 60 and 70 kN respectively act from the centre of a regular hexagon and act towards its six angular points. Find the magnitude and direction of the resultant of the forces.
Answer
A regular hexagon has six vertices. Let the centre be at the origin (0,0). The forces act from the centre towards the vertices. The angles of the vertices with respect to the positive x-axis are 0°, 60°, 120°, 180°, 240°, and 300°. Let the forces be F1=20, F2=30, F3=40, F4=50, F5=60, and F6=70 kN.
The components of the resultant force R are calculated as follows:
The magnitude of the resultant R is:
The direction θ with respect to the positive x-axis is:
Since both components are negative, the resultant lies in the third quadrant. The angle with the negative x-axis is 60°, so the resultant acts at 180° + 60° = 240° from the positive x-axis.
A lamp weighing 6 N is suspended from the ceiling by means of a wire. It is pulled to one side by a horizontal cord until the wire makes an angle of 45° with the ceiling. Find the tension in the wire and cord.
Answer
To find the tension in the wire and the cord, we analyze the equilibrium of the point where the lamp, wire, and cord meet. Let Tw be the tension in the wire and Tc be the tension in the horizontal cord.
The forces acting at the junction are:
- The weight of the lamp acting vertically downwards: W = 6 N.
- The tension in the horizontal cord acting to the side: Tc.
- The tension in the wire acting at an angle of 45° with the horizontal ceiling: Tw.
For the system to be in equilibrium, the sum of horizontal and vertical forces must be zero:
From the vertical equilibrium equation:
Substituting Tw into the horizontal equilibrium equation:
The tension in the wire is approximately 8.485 N, and the tension in the horizontal cord is 6 N.
A block weighing 600 N just starts moving down a rough inclined plane when supported by a force of 250 N acting parallel to the plane in the upward direction. The same block is on the verge of moving up the plane when pulled by a force by 350 N acting parallel to the plane. Find the inclination of the plane and coefficient of friction between the inclined plane and block.
Answer
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An I-section is made of top flanges 100×20 mm, web 100×200 mm and bottom flange 120×20 mm. Find the centroid of this section.
Answer
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A bar of T-section has flange 60 mm side and 15 mm thick. The web is 90 mm deep and 15 mm thick. Find the moment of inertia of section about centroidal axis XX and YY.
Answer
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A brass cone of base diameter 500 mm and height 300 mm is placed centrally on the top of the vertical Aluminium cylinder of diameter 500 mm and height 400 mm. Density of brass is 85 kN/m3 and density of Aluminum is 300 kN/m3. Determine the mass moment of inertia of composite body about vertical geometrical axis.
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The time required to stop the car
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The coefficient of friction between tyres and road.
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An elevator weighing 5000 N is moving with an acceleration of 4 m/sec2. During ascent, its operator having a weight of 600 N is standing on the scales placed on the floor. What is the scale reading? What will be the total tension in the cable of the elevator?
Answer
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