B.TECH R23 Engineering Mechanics Subject Important Questions
Note: Students, you should practice numerical problems from each unit with different variations of the given concepts.
UNIT I
2 Marks Questions:
- What are the types of friction?
- Define coefficient of friction and explain its significance.
- What is the cone of static friction? Draw a neat sketch.
5 Marks Questions:
- Define the following: (i) Angle of friction (ii) Limiting friction (iii) Cone of friction
- Derive the relationship between angle of friction and coefficient of friction.
- Explain Coulomb's laws of dry friction with practical applications.
- Describe the concept of impending motion and limiting friction with examples.
- What is a couple? State its properties. Distinguish between couple and moment.
- Classify different system of forces with suitable examples.
UNIT II
2 Marks Questions:
- Explain triangular law of forces.
- State Lami's theorem and mention its applications.
- What is the principle of virtual work? Give one example.
5 Marks Questions:
- A rigid body is subjected to three concurrent forces. If P=5kN, determine the magnitude of Q and R using triangle law of forces and Lami's theorem.
- Explain the method of joints for analyzing plane trusses with a numerical example.
- Derive the equations of equilibrium for spatial system of forces using vector approach.
- Apply the principle of virtual work to solve equilibrium problems of simple structures.
- Discuss the graphical method of finding resultant of coplanar forces.
- Determine the forces in all the members of the truss shown in the figure.
UNIT III
2 Marks Questions:
- State the location of centroid of semicircle arc whose radius is r with a sketch.
- Define polar moment of inertia and product of inertia.
- State Pappus theorems for surface area and volume.
5 Marks Questions:
- Determine the centroid of the section of the concrete dam as shown in the figure.
- Derive the formula for moment of inertia of a rectangular section about its centroidal axis.
- Find the centroid of a composite figure consisting of a rectangle with a semicircular cut-out.
- Explain the transfer theorem for moments of inertia with mathematical derivation.
- Locate the centre of gravity of the right circular cone of base radius r and height h.
- Calculate the moment of inertia of the shaded area about the x-axes and y-axes.
UNIT IV
2 Marks Questions:
- Distinguish between kinetics and kinematics.
- State D'Alembert's principle and its significance.
- Define work-energy theorem for a particle.
5 Marks Questions:
- A motion of a particle in rectilinear motion is defined by x = 2t³ - 8t² + 16t - 5. Determine the instants when velocity is zero and position at those instants.
- Apply work-energy method to solve problems involving variable forces acting on particles.
- Derive the equations of motion for curvilinear motion in terms of tangential and normal components.
- Explain impulse-momentum method and solve numerical problems involving impact.
- A bullet moving at 250 m/sec is fired into a log of wood and penetrates to a depth of 40 cm. Find the velocity with which it would emerge from a 20 cm thick similar piece.
- A stone is thrown upwards from the top of a 70 m high tower with velocity 19.2 m/s. Determine its position and velocity when t = 6 seconds.
UNIT V
2 Marks Questions:
- Analyze the impulse momentum equation.
- Differentiate between translation and rotation of rigid bodies.
- Define angular velocity and angular acceleration for rigid body rotation.
5 Marks Questions:
- A 5 kg steel ball strikes a wall with speed 15 m/sec at 60° angle. If contact time is 0.20 sec, find the average force exerted by the wall.
- Derive the equations of motion for a rigid body undergoing plane motion.
- Apply work-energy method to solve problems involving rotation of rigid bodies about fixed axis.
- Explain the kinematics of rigid body rotation and derive the relationship between linear and angular quantities.
- A 5 gm bullet is fired into a 1.5 kg wooden block. The block slides 0.25 m before stopping. Find the initial speed of the bullet (μ = 0.23).
- What is the difference between impulse and impulsive force? Deduce the relation between impulse and momentum.