JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I Year ENGINEERING MECHANICS Previous Question Paper (November/December - 2020 - R18)
Answer any five questions
All questions carry equal marks
Main
Two spheres, A and B, are resting in a smooth through as shown in figure 1. Draw the free body diagrams of A and B showing all the forces acting on them, both in magnitude and direction. Radius of spheres A and B are 250 mm and 200 mm, respectively.
Answer
To analyze the equilibrium of the two spheres, we identify the forces acting on each sphere. Let RA = 250 mm and RB = 200 mm be the radii of spheres A and B, and let WA and WB be their respective weights.
The forces acting on each sphere are:
- Sphere A:
- Weight (WA) acting vertically downwards through its center.
- Reaction force (N1) from the left inclined wall, acting perpendicular to the wall surface towards the center of A.
- Reaction force (N2) from the floor, acting vertically upwards at the point of contact.
- Interaction force (P) from sphere B, acting along the line joining the centers of the two spheres.
- Sphere B:
- Weight (WB) acting vertically downwards through its center.
- Reaction force (N3) from the right inclined wall, acting perpendicular to the wall surface towards the center of B.
- Reaction force (N4) from the floor, acting vertically upwards at the point of contact.
- Interaction force (P) from sphere A, acting along the line joining the centers of the two spheres (equal and opposite to the force exerted on A).
The line joining the centers of the spheres is inclined at an angle θ to the horizontal, where sin(θ) = (RA - RB) / (RA + RB) if the spheres are resting on a common horizontal plane, or determined by the geometry of the trough walls. The free body diagrams consist of the spheres represented as particles at their centers, with the weight vectors pointing down, reaction forces from the walls pointing normal to the surfaces, and the contact force P acting along the common normal at the point of contact between the spheres.
State the varignon’s theorem for system of forces in plane.
Answer
Varignon's theorem, also known as the principle of moments, states that the algebraic sum of the moments of a system of coplanar forces about any given point in their plane is equal to the moment of their resultant force about the same point.
Mathematically, if a system of forces F1, F2, ..., Fn acts in a plane and has a resultant R, then:
where d represents the perpendicular distance from the point to the line of action of each individual force, and D represents the perpendicular distance from the point to the line of action of the resultant force.
A circular roller of weight 1000 N and radius 20 cm hangs by a tie rod AB = 40 cm and rests against a smooth vertical wall at C as shown in figure 2. Determine the tension in the rod and reaction at point C.
Answer
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Two blocks A = 100 N and B = W are connected by a rod at their ends by frictionless hinges as shown in figure 3. Find the weight of block B (W) required for limiting equilibrium of the system if coefficient of friction at all sliding surfaces is 0.3.
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Three plates ABC and BCDE and DEF are welded together as shown in figure 4. Circle of diameter 1.5 m is cut from the composite plate. Determine the centroid of the remaining area.
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For the given shaded area shown in figure 5. Find MI about the reference axes i.e., Ox and Oy axis. All dimensions are in mm.
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Determine the mass moment of inertia of a quarter circular rod about x, y and z-axis as shown in figure 6.
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A mass m kg is acted on by a constant force of P Newton for t seconds. In this interval of time, it moves a distance x meter and acquires a velocity V m/s. Show that,
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A wagon weighing 500 kN starts from rest, runs 30 m down one percent grade and strikes the bumper post. If the rolling resistance of the track is 5 N/kN, find the velocity of the wagon when it strikes the post. If the bumper spring which compresses 1mm for every 15kN, determine by how much the spring will be compressed.
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