Roll No.
Total No. of Pages : 02
Total No. of Questions : 09
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B.Tech (Civil Engg.) (2018 Batch) (Sem.-1,2)
MECHANICS OF SOLIDS
Subject Code : BTPH-101-18
M.Code: 75351
Time: 3 Hrs. Max. Marks : 60
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INSTRUCTIONS TO CANDIDATES :
- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION - B & C have FOUR questions each.
- Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
- Select atleast TWO questions from SECTION - B & C.
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SECTION-A
- Write briefly : (2×10=20)
- Give the physical significance of gradient, divergence and curl of a field.
- Distinguish between conservative and non-conservative forces.
- Define Coriolis force.
- Distinguish between heavy, critical and light damping.
- Define quality factor for damped oscillations.
- Explain the concept of centre of mass.
- State theorems of parallel axes and perpendicular axes for moment of inertial.
- Write Euler's equations of motion.
- Write the laws of limiting friction.
- Explain stress-strain curve.
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SECTION-B
- a) Express gradient, divergence and curl of a field in spherical coordinates. 5
b) Find constants a, b and c so that the vector A = (x+2y+az)i +(bx-3y-z)j+(4x+cy+2z)k is irrotational, where i, j, k are rectangular unit vectors. 3 - a) State Newton's laws of motion and discuss their limitations in describing particle motion. 4
b) Discuss about the conservation of angular momentum and energy during the motion of a body. 4 - a) Derive a general differential equation of motion for a simple harmonic oscillator and obtain its solution. 5
b) The total energy of particle executing a S.H.M. of period 2p seconds is 10.24×10-4 Joule. The displacement of a particle at p/4 second is 0.08v2m. Find the amplitude and mass of the particle. 3 - a) Explain free vibrations, damped vibrations, forced vibrations and resonance, giving one example of each. 4
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b) Find the maximum velocity and acceleration of a particle executing S.H.M. of period 10p seconds and amplitude 5×10-2m. 4
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SECTION-C
- a) Define a rigid body. Prove that the total internal forces and torques for these forces are always zero. 4
b) Prove that angular momentum of a system of particles can be expressed as the sum of angular momentum of the system of centre of mass and angular momentum of system about the centre of mass. 4 - a) Derive the expression for moment of inertia of a plane lamina about an axis lying in its plane parallel to one of its sides and passing through its centre of mass. 4
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b) A uniform thin bar of mass M and length L is bent to make a square. Calculate its moment of inertia about an axis passing through the centre of mass perpendicular to the square thus formed. 4 - a) Define angle of friction and angle of repose (with neat diagrams) and derive relation between them. 4
b) “Friction is a necessary evil”, comment on this statement. Give some methods to reduce friction. 4 - a) Distinguish between the concepts of elasticity and plasticity with appropriate examples. 4
b) Differentiate between bending moment and twisting moment. 4
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NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.
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