Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer/answer the following (Any seven
only):
Define a conservative force. How is it related to the potential energy function?
Write the expression of Newton's second law in polar coordinates.
What is the physical significance of the gradient of a potential energy function?
State Euler's laws of motion for a rigid body.
Define a planar rigid body. Give an example.
Explain the difference between limiting and non-limiting friction.
Name the two main types of joints used in trusses.
Define a free body diagram.
Define normal stress and shear stress.
What is the use of Mohr's circle in stress analysis?
Q.2 Solve both questions :
State and explain the form invariance of Newton's second law.
Prove that the curl of a conservative force field is zero.
Q.3 Solve both questions :
A particle moves under a central force $ F(r)=-k/r^{2} $. Derive the expression for effective potential energy and sketch the energy diagram for different types of orbits.
A satellite is in circular orbit around Earth. If its radius is increased by 5%, calculate the change in its orbital speed. Use Kepler's third law to justify the result.
Q.4 Solve both questions :
Explain the motion of a rigid body in a plane with suitable examples.
A uniform disc of mass 2 kg and radius 0.5 m is rotating about its center with an angular velocity of $ 10~rad/s $. Find its angular momentum.
Q.5 Solve both questions :
What is the angular momentum of a rigid body in planar motion about a fixed point? Derive the expression and explain its physical significance.
A rigid body is rotating with an angular velocity of $ 5~rad/s $. If the moment of inertia about the axis is $ 2~kg\cdot m^{2} $, calculate the torque required to stop it in 4 seconds.
Q.6 Solve both questions :
What is a truss? Describe how a perfect truss differs from a redundant and a deficient truss with examples.
A light rod AB is supported by a hinge at A and a roller at B. A force of 500 N is applied at 2 m from A inclined at $ 30^{\circ} $ to the horizontal. Determine the reactions at the supports using a free body diagram.
Q.7 Solve both questions :
What is strain energy? Derive an expression for the strain energy stored in a prismatic bar under axial load.
Draw shear force and bending moment diagrams for a simply supported beam of 6m span carrying a point load of 10 kN at 2m from the left end.
Q.8 Solve both questions :
A circular shaft of diameter 60 mm is subjected to a torque of 1500 Nm. Determine the shear stress at the outer surface of the shaft and the angle of twist over a length of 2 m. Take G = 80 GPa.
State and derive the generalized Hooke's Law for an isotropic material under three-dimensional stress. Include the effect of thermal strain in your explanation.
Q.9 Write short notes on any two of the following:
Coriolis acceleration
Foucault's Pendulum
Strain hardening
Castigliano's Theorem
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer/answer the following (Any seven
only):
Define a conservative force. How is it related to the potential energy function?
Write the expression of Newton's second law in polar coordinates.
What is the physical significance of the gradient of a potential energy function?
State Euler's laws of motion for a rigid body.
Define a planar rigid body. Give an example.
Explain the difference between limiting and non-limiting friction.
Name the two main types of joints used in trusses.
Define a free body diagram.
Define normal stress and shear stress.
What is the use of Mohr's circle in stress analysis?
Q.2 Solve both questions :
State and explain the form invariance of Newton's second law.
Prove that the curl of a conservative force field is zero.
Q.3 Solve both questions :
A particle moves under a central force $ F(r)=-k/r^{2} $. Derive the expression for effective potential energy and sketch the energy diagram for different types of orbits.
A satellite is in circular orbit around Earth. If its radius is increased by 5%, calculate the change in its orbital speed. Use Kepler's third law to justify the result.
Q.4 Solve both questions :
Explain the motion of a rigid body in a plane with suitable examples.
A uniform disc of mass 2 kg and radius 0.5 m is rotating about its center with an angular velocity of $ 10~rad/s $. Find its angular momentum.
Q.5 Solve both questions :
What is the angular momentum of a rigid body in planar motion about a fixed point? Derive the expression and explain its physical significance.
A rigid body is rotating with an angular velocity of $ 5~rad/s $. If the moment of inertia about the axis is $ 2~kg\cdot m^{2} $, calculate the torque required to stop it in 4 seconds.
Q.6 Solve both questions :
What is a truss? Describe how a perfect truss differs from a redundant and a deficient truss with examples.
A light rod AB is supported by a hinge at A and a roller at B. A force of 500 N is applied at 2 m from A inclined at $ 30^{\circ} $ to the horizontal. Determine the reactions at the supports using a free body diagram.
Q.7 Solve both questions :
What is strain energy? Derive an expression for the strain energy stored in a prismatic bar under axial load.
Draw shear force and bending moment diagrams for a simply supported beam of 6m span carrying a point load of 10 kN at 2m from the left end.
Q.8 Solve both questions :
A circular shaft of diameter 60 mm is subjected to a torque of 1500 Nm. Determine the shear stress at the outer surface of the shaft and the angle of twist over a length of 2 m. Take G = 80 GPa.
State and derive the generalized Hooke's Law for an isotropic material under three-dimensional stress. Include the effect of thermal strain in your explanation.
Q.9 Write short notes on any two of the following:
Coriolis acceleration
Foucault's Pendulum
Strain hardening
Castigliano's Theorem