Mechanics Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Which of the following is the basic law for mechanics?

1. Parallelogram law
2. Hooke’s law
3. Newton’s law of viscosity
4. Newton’s laws of motion

Ans. The correct answer is d. Newton’s Laws of Motion

Explanation: Newton's laws of motion are the fundamental basis of mechanics. Newton's first, second, and third laws are commonly used to deal with mechanical problems.

Ques. Which of the following is the condition for the three-force theorem in mechanics?

1. The system should be co-planar, parallel
2. The force system should be in equilibrium only
3. The force system should be in equilibrium, co-planar, concurrent, or parallel
4. The force systems should be non-coplanar

Ans. The correct answer is c. The force system should be in equilibrium, co-planar, concurrent, or parallel

Explanation: According to the three-force theorem when three forces act on a body, the force systems are in equilibrium, coplanar, and either concurrent or parallel.

Ques. Which of the following is a branch of mechanics?

1. Statics and dynamics
2. Kinetics and kinematics
3. Kinematics and dynamics
4. Statics and kinetics

Ans. The correct answer is a. Statics and dynamics

Explanation: Statics and dynamics are the branches of mechanics. Statics is the study of bodies that are at rest. The study of bodies in motion is known as dynamics.

Ques. Which of the following is not a parameter of motion?

1. Atomic structure
2. Velocity
3. Speed
4. Time

Ans. The correct answer is a. Atomic structure

Explanation: Atomic structure is not a parameter of motion.

Ques. Which of the following statements describes the resultant of two forces?

1. Force that has the same effect as the two forces
2. Force that maintains the system in equilibrium
3. Force that has the highest magnitude in the system
4. Force that has the same effect as one force

Ans. The correct answer is a. Force that has the same effect as the two forces

Explanation: When two forces act on a body, the sum of the two forces is considered. The resultant force has the same impact as the original two forces. The resultant of the two forces is the force that has the same impact as the two forces.

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Short Answers Questions [2 Marks Questions]

Ques. What is mechanics?

Ans. Mechanics is the branch of physics that deals with the study of motion when subjected to forces or displacements, as well as the effect of the bodies on their surroundings.

Ques. Define fluid mechanics.

Ans. The study of fluid mechanics is concerned with the reaction of fluids to forces applied to them. It is considered to be a branch of classical physics with important applications in hydraulic and aeronautical engineering, as well as chemical engineering, meteorology, and zoology.

Ques. What is relativistic mechanics?

Ans. The term relativistic mechanics refers to mechanics that are consistent with special and general relativity. In conditions when the velocities of moving objects are comparable to the speed of light c, it gives a non-quantum mechanical explanation of a particle system or a fluid.

Ques. What are the applications of statistical mechanics? 

Ans. Statistical mechanics, also known as statistical thermodynamics, allows for the calculation of macroscopic (bulk) characteristics of pure substances and mixtures using microscopic properties of molecules and their interactions.

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Long Answers Questions [3 Marks Questions]

Ques. What are the different branches of mechanics?

Ans. Mechanics is classified into three categories:

• Statistical mechanics: Statistical mechanics is a branch of physics theory that studies the application of probability theory as well as the average or mean behavior of a mechanical system whose state is considered to be uncertain. This machine is commonly used in the thermodynamic accomplishment of huge systems.
• Classical mechanics: Classical mechanics is a branch of physics that deals with the description and explanation of the motion of point-like, extended material, and deformable objects in three-dimensional Euclidean space. It uses fundamental concepts about the existence and interaction of matter and forces. It accepts the existence of distinct observable qualities for matter and energy.
• Quantum mechanics: Quantum mechanics is a branch of physics concerned with the behavior of matter and light at the subatomic and atomic levels. It attempts to explain the characteristics of atoms and molecules, as well as the basic particles that make them up, such as protons, neutrons, electrons, gluons, and quarks.

Ques. What are the branches of classical mechanics?

Ans. The following are the branches of classical mechanics

• Kinematics: Kinematics is the study of mechanical points, bodies, and systems in their motion without regard for their related physical qualities or the forces acting on them. The study is known as geometry of motion, and it mathematically describes these motions using algebra.
• Statics: The branch of mechanics that deals with bodies at rest or forces in equilibrium is known as statics. A physical state in which the net force through the system is zero and the system's components are at rest is referred to as static equilibrium.
• Dynamics: Dynamics is a branch of mechanics that deals with the study of the forces that influence the motion of moving objects and systems. It comprises a few basic concepts like force, mass, length, and time.

Ques. What are the various applications of mechanics in real life?

Ans. The following are the applications of mechanics in real life

• Manufacturing: The concepts of motion control, vibration, and thermodynamics are applied in the design and operation of machinery and equipment in mechanics.
• Construction:  The concepts of stress, strain, and stability are used in mechanics for the construction and study of structures including bridges, buildings, and towers.
• Robotics: The concepts of motion control, sensing, and manipulation all are applied in the design, manufacture, and operation of robots in mechanics.
• Environmental Uses: The concepts of fluid dynamics, heat transport, and solid mechanics all play a part in understanding the physical processes of the atmosphere, seas, and land.

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Very Long Answers Questions [5 Marks Questions]

Ques. What is the failure of classical mechanics?

Ans. Even though classical mechanics can explain most events in everyday life, there are a few examples when classical mechanics fails to provide a proper/correct explanation. A few examples of the failure of classical mechanics are

• Black body radiation: According to classical mechanics, the electromagnetic radiation emitted by a black body can have any wavelength. This is not correct since the wavelength range is determined by the frequency or wavelength of the electromagnetic wave and is released as discrete packets of light known as photons.
• Photoelectric effect: In the process of the photoelectric effect, light incident on metal causes electron emission. According to classical physics, the energy in electromagnetic waves is continuous and depends on the intensity of light; so, emitting electrons from a dim light should take some time. However, this is not the case since light contains distinct energy that varies with frequency.
• Hydrogen atom: Electrons orbiting around the hydrogen nucleus constantly change direction and hence accelerate. An accelerating charged particle would produce electromagnetic radiation and hence lose energy, according to classical mechanics. As a result, the electrons would finally lose all of their energy and collide with the nucleus. However, we all know that this is not the case.

Ques. A steel rod 2.0 m long has a cross-sectional area of 0.30 cm². The rod is now hung by one end from a support structure, and the 550 kg milling machine is hung from the rod’s lower end. Determine the 

1. Stress
2. Strain, and 
3. The elongation of the rod.

Ans. Given

• The original length of the rod, L_o = 2 m
• Area of the cross-section of the rod, A = 0.30 cm² = 0.30 x 10^-4 m²
• Mass of the milling machine attached to the lower end of the rod, m = 550 kg

Force acting on the rod in a downward direction due to the hanging milling machine is given by

F = mg = 550 x 9.8 = 5390 N

1. Stress on the rod is given by

Stress = Force/Area

⇒ Stress = (5390)/(0.30 x 10^-4) = 1.8 x 10⁸ Pa

2. The strain produced in the steel rod is given by

Strain = Stress/Young’s modulus (Y)

Young’s modulus for the steel rod is equal to 2 x 10¹¹ Pa

On substituting the values, we get

Strain = (1.8 x 10⁸)/(2 x 10¹¹) = 9 x 10^-4

100. Elongation of the rod is given by

ΔL = Strain x Original length L_o

⇒ ΔL = 9 x 10^-4 x 2 = 1.8 mm

Ques. A steel wire 4.0 m in length is stretched through 2.0 mm. The cross-sectional area of the wire is 2.0 mm². If Young’s modulus of steel is 2 x 10¹¹ Nm^-2, find

1. The energy density of the wire
2. The elastic potential energy stored in the wire

Ans. Given

• The original length of the steel wire, L₀ = 4.0 m
• Increased in the length of the wire, ΔL = 2 mm = 2 x 10^-3 m²
• Area of the cross-section of the wire, A = 2 mm² = 2 x 10^-6 m²
• Young’s modulus of steel, Y = 2 x 10¹¹ N m^-2

The strain produced in the wire is given by

Strain = Change in length ΔL / Original length L₀

⇒ Strain = (2 x 10^-3)/(4) = 0.5 x 10^-3

Stress on the wire is given by

Stress = Young’s modulus x Strain

⇒ Stress = 2 x 10¹¹ x 0.5 x 10^-3 = 10⁸ N m^-2

1. Energy density of the wire is given by (ΔU/Volume)

Energy density = 1/2 x Stress x Strain

⇒ Energy density = 1/2 x 10⁸ x 0.5 x 10^-3

⇒ Energy density = 2.5 x 10⁴ J/m³

2. Elastic potential energy is given by

ΔU = Energy density x Volume

⇒ ΔU = Energy density x Area of cross-section x Length

⇒ ΔU = 2.5 x 10⁴ x 2 x 10^-6 x 4 = 0.20 J

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