JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I ENGINEERING MECHANICS Previous Question Paper (May - 2019 - R18)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
PART - A
State Varignon’s theorem.
Answer
Varignon's theorem, also known as the principle of moments, states that the moment of a force about any point is equal to the algebraic sum of the moments of its components about the same point. Mathematically, if a force F is resolved into components F1 and F2, then the moment MO about a point O is given by:
Distinguish types of friction.
Answer
Friction is primarily categorized into two main types based on the state of motion of the bodies involved:
- Static Friction: The resistance force that acts between two surfaces in contact that are at rest relative to each other. It prevents the initiation of motion and varies in magnitude up to a maximum value known as limiting friction.
- Dynamic (or Kinetic) Friction: The resistance force that acts between two surfaces in contact when one is sliding over the other. It is further subdivided into sliding friction, which occurs during relative motion, and rolling friction, which occurs when one body rolls over the surface of another.
What is product of inertia illustrate with example.
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State the principle of impulse-momentum.
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Write work energy equation for rotating bodies.
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Discuss the equations of equilibrium for coplanar system of forces.
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State and explain Pappus theorem II.
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What is perpendicular axis theorem?
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Define normal and tangential accelerations of a particle.
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Explain D’Alembert’s principle in plane motion.
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PART - B
Find the magnitude of forces F1 and F2 if they act at right angle, their resultant is 34 N. If they act at 60 degrees, their resultant is 7 N.
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A 75 N vertical force is applied to the end of a pole 3 m long which is attached to a shaft at O. Determine:
- The moment of the 75N force about O,
- The magnitude of the horizontal force applied at A which creates the same moment about O,
- The smallest force applied at A which creates the same moment about O,
- How far from the shaft at O a 200 N vertical force must act to create the same moment about O?
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To move a boat uniformly along the river at a given speed, a resultant force R = 520N is required. Two men pull with force P and Q, by means of ropes, to do this. The ropes makes an angle of 30 and 40 degrees respectively with the sides of the river. Determine the force P and Q, If θ1 = 30, find the value of θ2 such that the force in the rope Q is minimum. What is the minimum force Q?
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A 30 kg collar may slide on frictionless vertical rod and is connected to a 34 kg counter weight. Find the value of h for which the system is in equilibrium.
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Two blocks W1 and W2 which are connected by a horizontal bar AB are supported on rough planes. The coefficient of friction for the block A = 0.4. The angle of friction for the block B is 20 degrees. Find the smallest weight W1 of the block A for which the equilibrium can exist, if W2 = 2250 N.
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A thin homogeneous semi circular plate of radius r is suspended from its corner A. Find the angle made by its straight edge AB with the vertical.
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Two blocks W1 and W2 resting on two inclined planes, are connected by a horizontal bar AB. If W1 equals 1000 N, determine the maximum value of W2 for which the equilibrium can exist. The angle of limiting friction is 20 degrees at all rubbing faces.
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Find the coordinates of the centroid of the area shown. All dimensions are in mm.
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Find the Moment of Inertia (MI) about the centroidal axis.
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Determine the mass moment of inertia of a circular plate of uniform thickness, about centroidal axes.
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Find the MI about the centroidal axis and about xy axis for the given figure. All dimensions are in mm.
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A railway car is moving with a velocity of 20m/s. The diameter of the wheel is 1m. The wheel is running on a straight rail without slipping. Find the velocity of the point on the circumference at 60 degrees in the clockwise direction from the top at any instant.
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A 600mm diameter flywheel is brought uniformly from rest to a speed of 350 rpm in 20 seconds. Determine the velocity and acceleration of a point on the rim 2 seconds after starting from rest.
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Find the least initial velocity with which a projectile is to be projected so that it clears a wall 4m height located at a distance of 5m, and strikes the ground at a distance 4m beyond the wall. The point of projection is at the same level as the foot of the wall.
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A ball drops from the ceiling of a room and after rebounding twice from the floor reaches a height equal to one-fourth of the height of the ceiling. Show that the coefficient of restitution is 0.707.
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A body weighing 20 N is projected up a 20 degree inclined plane with a velocity of 12 m/s, coefficient of friction is 0.15. Find the maximum distance the body will move up the inclined plane.
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Two blocks of weights P and Q are connected by a flexible but inextensible cord. If the coefficient of friction between the block P and the horizontal surface is μ and all other friction is negligible, find (i) the acceleration of the system and (ii) the tensile force S in the cord. The following numerical data are given: P = 54 N ; Q = 25 N; μ = 1/3.
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Determine the constant force P that will give the system of bodies a velocity of 3m/sec after moving 4.5m from rest. Coefficient of friction between the blocks and the plane is 0.3. Pulleys are smooth.
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