HSBTE Applied Physics, February 2023 Examination, Fierst Semester Diploma in Engineering,  Question Paper and Answers.

HSBTE Exam February 23Time : 3 Hrs. M.M.: 60

1st Sem. / (NEP) Subject: Applied Physics-I 220013/210013

SECTION-A

Note: Multiple choice questions. All questions are compulsory (6x1=6)

Q.1 Newton is the SI unit of

• a) Mass   b) distance   c) Velocity   d) Force

Ans: d) Force

Note: The Newton (symbol: N) is the SI (International System of Units) unit of force.

Q.2 The Formula for scalar product is

• a) A.B = |A| |B| cos ᶿ      b) F = m a    c) A x B = |A| |B| sinᶿ     d) None of above

Ans: a) A.B = |A| |B| cos θ

Q.3 The energy due to the position of the body is called

• a) Potential energy    b) Kinetic energy    c) transformation of energy    d) None of the above

Ans: a) Potential energy

Note: The energy due to the position of a body is called potential energy. So, the correct answer is (a)

Q.4 Stress is directly proportional to strain is called

• a) Newton's law    b) Viscosity     c) Hooks law    d) surface tension

Ans: c) Hooke's Law

Note: Hooke's Law states that stress is directly proportional to strain within the elastic limit of a material. So, the correct answer is (c) Hooke's Law.

Q.5 The quantities which have only magnitude and no direction are called

• a) Vector quantity    b) Scalar quantity    c) Physical quantity    d) None of the above

Ans: b) Scalar quantity

Note: Quantities that have only magnitude and no direction are called scalar quantities. So, the correct answer is (b) Scalar quantity

Q.6 The unit of power is

• a) Watt b) Meter c) Second d) Joule

Ans: a) Watt

Note: The unit of power is the watt (symbol: W). So, the correct answer is (a) Watt.

SECTION-B

Note: Objective/ Completion type questions. All questions are compulsory. (6x1=6)

Q.7 The dimensional formula for velocity is _______

Ans: M0 L1 T-1

• M = Mass

• L = Length

• T = Time

This indicates that velocity is dimensionally represented as M0 L1 T-1 meaning it has dimensions of length per unit time.

Q.8 Define the resolution of force.

Ans: The resolution of a force refers to breaking down a force into its components along specified axes. This process involves determining the effect of a force in different directions. In a two-dimensional system (such as the x and y axes), a force F can be resolved into horizontal (Fx) and vertical (Fy) components. Mathematically, if θ is the angle between the force vector and a chosen axis, the resolution can be expressed as:

• Fx.​= F⋅cos(θ)

• Fy = F⋅sin(θ)

These components allow for a more detailed analysis of the effects of the force in different directions, It is useful in physics and engineering problems involving motion, equilibrium, and other force-related phenomena.

Q.9 Define Frequency

Ans: Frequency refers to the number of occurrences of a repeating event per unit of time. The standard unit of frequency in the International System of Units (SI) is the hertz (Hz), where one hertz is equivalent to one cycle per second.

Mathematically, frequency (f) can be defined as:

• f = 1/T

• f is the frequency, T is the period of the event.

The period (T) is the time it takes for one cycle of the event to occur. It is commonly used in the context of waves, oscillations, sound, electromagnetic signals, and many other cyclic processes

Q.10 Define Negative Work

Ans: Negative work occurs when the force applied to an object is in the opposite direction to the displacement of the object. In other words, when force and displacement are in opposite directions, the work done by the force is considered negative.

The formula for Negative work (W) is given by:     W = F⋅d⋅cos(θ)

• F is the force applied,

• d is the displacement of the object,

• θ is the angle between the force vector and the displacement vector.

Note: If the angle θ is 180 degrees (indicating opposite directions), the cosine of 180 degrees is -1. Therefore, the work done (W) will be negative in this case. It indicates that the force is acting against the direction of motion or displacement.

Negative work does not mean that energy is "lost". It means the energy is transferred to another form or is used to do work against the applied force. It is important to consider both the direction of the force and the direction of the displacement to determine whether the work done is positive or negative.

Q.11 Define Torque

Ans: Torque, also known as the moment of force. “It is a measure of the tendency of a force to rotate an object about an axis or pivot point”.

Note: It is a vector quantity, meaning it has both magnitude and direction. Torque is mathematically defined as the product of the force applied and the perpendicular distance from the axis of rotation to the line of action of the force. The formula for torque (τ) is given by:

• τ = r⋅F⋅sin(θ)

• τ is the torque,

• r is the distance from the axis of rotation to the point where the force is applied (lever arm),

• F is the magnitude of the force applied,

• θ is the angle between the lever arm and the direction of the applied force.

The SI unit of torque is the newton-meter (N·m).

Note: Torque causes angular acceleration in objects. It is also involved in the equilibrium of rotating objects, influencing their stability and behavior. In engineering and physics, torque is a key concept in understanding the motion of machinery, vehicles, and various mechanical systems.

Q.12 Define Co-linear vector

Ans: “Co-linear vectors are vectors that lie along the same straight line or parallel lines”.

For two vectors A and B to be co-linear, there must exist real numbers k and m such that A=k⋅B

k is a scalar. This equation indicates that A is a scalar multiple of B, meaning they have the same directions (ifk>0) or opposite (if k<0) directions.

Note: In other words, two or more vectors are said to be co-linear if they have the same or opposite directions. It is represented by a single line of action. The magnitudes of co-linear vectors may or may not be equal.

In three-dimensional space, three vectors are co-linear if they all lie along the same line or parallel lines.

Co-linear vectors are a special case of parallel vectors where the vectors share the same line of action

SECTION-C

Note: Short answer type questions. Attempt any eight questions out of ten questions. (8x4=32)

Q.13 Check the correctness of

a) v2 -u2 = 2 a s                b) v = u + a t

Ans: The correctness of the given equations:

a) v2 -u2 = 2 a s

This equation is a kinematic equation that relates initial velocity (u), final velocity (v), acceleration (a), and displacement (s). It is correct and corresponds to one of the equations of motion under constant acceleration. The correct form is: v2 -u2 = 2 as. So, option (a) is correct.

b) v = u + a t This equation is also a kinematic equation that relates initial velocity (u), final velocity (v), acceleration (a), and time (t). The correct form is v = u + a t. So, option (b) is correct.

Both equations are correct and correspond to the equations of motion under constant acceleration

Q.14 Define fundamental and derived quantities. Give two examples of each.

Ans: “Fundamental quantities are basic physical quantities that are independent and cannot be defined in terms of other physical quantities”. The measurement of these quantities forms the foundation of the measurement system. The International System of Units (SI) defines seven fundamental quantities. Here are two examples:

• 1. Length (L): The fundamental quantity that expresses the extent of an object in one dimension. The SI unit of length is the meter (m).

• 2. Time (T): The fundamental quantity that represents the progression of events from the past through the present to the future. The SI unit of time is the second (s).

Derived Quantities: Derived quantities are physical quantities that are defined in terms of one or more fundamental quantities. They are derived through mathematical combinations of fundamental quantities. Here are two examples:

• 1. Speed (v): Derived from the fundamental quantities of length and time. Speed is the rate of change of distance for time. The SI unit of speed is meters per second (m/s).

• 2. Acceleration (a): Derived from the fundamental quantities of length and time. Acceleration is the rate of change of velocity for time. The SI unit of acceleration is meters per second squared (m/s²).

Note: fundamental quantities are the basic building blocks of a measurement system. Derived quantities are formed by combining fundamental quantities in various ways to describe other aspects of the physical world.

Q.15 Define angular velocity and angular acceleration. Give a formula for both.

Ans: Angular Velocity: Angular velocity (ω) is a measure of the rate at which an object rotates or revolves around a fixed point or axis. It is the angular displacement per unit of time. Mathematically, angular velocity is given by the formula:

• ω=ΔtΔθ​

• ω is the angular velocity,

• Δθ is the change in angular displacement,

• Δt is the change in time.

• The SI unit of angular velocity is radians per second (rad/s).

Angular Acceleration: Angular acceleration (α) is the rate at which the angular velocity of an object changes over time. It describes how quickly or slowly an object is speeding up or slowing down in its rotation. The formula for angular acceleration is: α=ΔtΔω​

• α is the angular acceleration,

• Δω is the change in angular velocity,

• Δt is the change in time.

The SI unit of angular acceleration is radians per second squared (rad/s²).

Note: Angular velocity measures the rotational speed of an object. Angular acceleration measures how quickly or slowly that rotational speed is changing.

Q.16 Define kinetic energy. Derive an expression for it.

Ans: Kinetic energy is the energy possessed by an object due to its motion. The amount of kinetic energy of an object depends on its mass and its speed. The kinetic energy of an object increases with both mass and the square of its velocity.

Derivation of the Kinetic Energy Formula:

The kinetic energy (KE) of an object is derived by using the work-energy theorem. The work (W) done on an object is equal to the change in its kinetic energy. The work done by a force (F) acting on an object over a displacement (d) is given by W=F⋅d.

According to the work-energy theorem, this work done is equal to the change in kinetic energy: W=ΔKE

Now, the work done by a force can also be expressed as the product of the force and the displacement. Here the force is the net force acting on the object and the displacement is in the direction of the force:

• W=F⋅d

Equating the two expressions for work: ΔKE=F⋅d

Now, the acceleration (a) of an object can be related to force and displacement using Newton's second law (F=m⋅a). The displacement (d) is expressed in terms of initial velocity (u), final velocity (v), and acceleration (a):

• ΔKE=m⋅a⋅d

• ΔKE=m⋅a⋅(v−u)

Now, using the kinematic equation v=u+a⋅t (where v is final velocity, u is initial velocity, "a" is acceleration, and t is time), we can express "a" as ΔtΔv​:

• ΔKE=m⋅ΔtΔv​⋅(v−u)

Now, considering Δt approaching zero (0limΔt→0​), we get: ΔKE=m⋅v

This is the expression for kinetic energy (KE):

• KE=1/2​mv2

So, the kinetic energy of an object is directly proportional to the square of its velocity and is given by the formula 2KE=1/2​mv2,

Here m is the mass of the object and v is its velocity.

Q.17 Define Centripetal and Centrifugal force. Give formulas for each.

Ans:

Centripetal Force: “Centripetal force is the force that acts on an object moving in a circular path, directed toward the center of the circle or the axis of rotation”. Its primary purpose is to keep the object in circular motion by constantly changing its direction. The formula for centripetal force (Fc​) is given by: Fc​=rm⋅v2​

• Fc​ is the centripetal force,

• m is the mass of the object,

• v is the speed of the object,

• r is the radius of the circular path.

Centrifugal Force: Centrifugal force is referred to as a "fictitious" or "pseudo" force. Centrifugal force in the circular motion acts outward from the center of rotation”. It acts opposite to the centripetal force. It is treated as the negative of the centripetal force:

• centrifugal force =−centripetal (Fcentrifugal​= −Fcentripetal)​

Note: It's important to note that centrifugal force does not result from any physical interaction. It is a result of viewing the motion from a non-inertial (accelerated) frame. In an inertial frame, no outward force is acting on the object.

Centripetal force is a real force acting toward the center of rotation, keeping an object in circular motion. Centrifugal force is a pseudo force that appears to act outward in a rotating reference frame. The two forces are related by Newton's third law, but centrifugal force is not a true force in the classical sense.

Q.18 Write a short note on the transformation of energy.

Ans: The transformation of energy is the conversion of energy from one form to another. In any physical process or system, energy can change from one type to another. While the total energy of the system remains constant, as said by the principle of conservation of energy. This concept is fundamental to understanding the various ways in which energy is utilized, transferred, and distributed in the natural world.

The following are points regarding the transformation of energy:

• a. Conservation of Energy: The law of conservation of energy states that the total energy of an isolated system remains constant over time. Energy cannot be created or destroyed. It can only change forms.

• b. Forms of Energy: Energy exists in various forms such as kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), chemical energy, electrical energy, and others. The transformation of energy involves the conversion between these different forms.

• c. Examples of Energy Transformation:

  • Mechanical to Thermal: When an object is rubbed or friction is applied, mechanical energy is transformed into thermal energy (heat).

  • Chemical to Thermal: Combustion of fuel is an example where chemical energy is transformed into thermal energy and mechanical energy as well.

  • Potential to Kinetic: An object falling under gravity transforms potential energy into kinetic energy.

• d. Efficiency of Energy Transformation: In practical systems, not all of the energy input is converted into the desired form. Some energy is often lost as waste heat or other forms. The efficiency of an energy transformation process is the ratio of useful output energy to the input energy.

• e. Renewable Energy Transformation: In the context of sustainable energy, there is a focus on transforming energy from renewable sources such as sunlight, wind, and water into usable forms like electricity. These processes contribute to reducing dependence on non-renewable resources.

Q.19 Explain in short Absolute pressure.

Ans: Absolute pressure is the total pressure exerted by a fluid, including both atmospheric pressure and the pressure exerted by the fluid itself. It is measured relative to a vacuum. Absolute pressure is the pressure of the fluid in addition to the atmospheric pressure that acts on the fluid.

• The formula for absolute pressure (Pabsolute​)

• Pabsolute​=Patmospheric​+Pgauge​

  • · Pabsolute​ is the absolute pressure.

  • · Patmospheric​ is the atmospheric pressure. Atmospheric pressure is the pressure exerted by the Earth's atmosphere at a given location.

  • · Pgauge​ is the gauge pressure. Gauge pressure is the pressure measured above atmospheric pressure (if positive) or below atmospheric pressure (

When measuring pressure, devices like pressure gauges display gauge pressure. To obtain absolute pressure, atmospheric pressure must be added.

Absolute pressure is important in various engineering and scientific applications such as in fluid dynamics, and thermodynamics. The measurements involve pressure-sensitive instruments. It provides a complete measure of the total pressure experienced by a fluid. It is crucial for accurate calculations and analysis in many fields.

Q.20 Explain Young’s Modulus and Bulk’s Modulus with formulas.

Ans: Young's Modulus is also known as the modulus of elasticity. It is a measure of the rigidity of a material. It measures the ability of a material to deform under an applied load and then return to its original shape when the load is removed. Young's Modulus is denoted by the symbol E, Tts formula is given by: E=Strain/Stress​

Mathematically, it can also be expressed as:

• E= Force(F)/ Area(A) X Original Length(L0​)/ Change in Length(ΔL)

  • · E is Young's Modulus,

  • · Stress is the applied force per unit area (force/area),

  • · Strain is the resulting deformation or change in length per unit of original length (change in length/original length).

Young's Modulus is typically measured in Pascals (Pa) or N/m²

Bulk Modulus (K): Bulk Modulus measures the resistance of a material to uniform compression or a decrease in volume when subjected to external pressure. It is relevant for materials that experience changes in volume but do not undergo shear deformation. Bulk Modulus is denoted by the symbol K, and its formula is given by: K=−Change in Pressure/Volumetric Strain​

Mathematically, it can also be expressed as:

• K=− ΔP/Δv/ v

  • K is the Bulk Modulus,

  • ΔP is the change in pressure,

  • Δv/V​ is the volumetric strain (change in volume/original volume).

Bulk Modulus is measured in Pascals (Pa) or N/m².

Conclusion: Young's Modulus characterizes the stiffness of a material under tension. Bulk Modulus characterizes its resistance to volume changes under pressure. Both properties are important in materials science and engineering. They help to understand and predict the behavior of materials under different types of mechanical loads.

Q.21 Explain in short Gauge pressure.

Ans: Gauge pressure is the pressure measured above atmospheric pressure. It represents the pressure of a fluid or gas relative to the atmospheric pressure at a specific location. In most pressure-measuring devices, such as pressure gauges, the reading displayed is gauge pressure.

The formula for gauge pressure (Pgauge​) is: Pgauge​=Pabsolute​−Patmospheric​

Pgauge​ is the gauge pressure,

Pabsolute​ is the absolute pressure (including atmospheric pressure),

Patmospheric​ is the atmospheric pressure.

If the gauge pressure is positive, it means the pressure is above atmospheric pressure. If it's negative, it indicates a pressure lower than atmospheric pressure.

For example, if a pressure gauge reads 300 kPa, and the atmospheric pressure is 100 kPa, the gauge pressure would be 200 kPa (300 kPa - 100 kPa). This value represents the pressure exerted by the fluid or gas above and beyond the atmospheric pressure.

Gauge pressure is important in applications where absolute pressure is not the primary concern. It is commonly used in fields such as fluid mechanics, engineering, and industrial processes.

Q.22 Explain heat and temperature on the basis of kinetic Theory.

Ans: The kinetic theory of matter is a model to explain the behavior of matter in terms of the motion of its constituent particles, such as atoms and molecules. This theory provides a foundation for understanding the concepts of heat and temperature.

Heat: In the kinetic theory, heat is interpreted as the kinetic energy associated with the random motion of particles within a substance. According to this theory, the higher the temperature of a substance, the greater will be the average kinetic energy of its particles. When heat is added to a substance, it is absorbed by the particles. This causes particles to move more vigorously. on the other hand, when heat is removed, the particles lose kinetic energy and the substance cools down.

The relationship between heat (Q), mass (m), specific heat capacity (c), and temperature change (ΔT) is expressed by the equation:

• Q=mcΔT

• · Q is the heat transferred,

• · m is the mass of the substance,

• · c is the specific heat capacity of the substance,

• · ΔT is the change in temperature.

This equation highlights that the heat transferred is proportional to the mass, specific heat capacity, and temperature change.

Temperature: In the kinetic theory, temperature is a measure of the average kinetic energy of the particles in a substance. The higher the temperature, the greater will be the average kinetic energy of the particles. Temperature is dependent on the average kinetic energy per particle not on the total kinetic energy.

The Kelvin scale is often used in the kinetic theory. It is directly proportional to the average kinetic energy of the particles. The relationship between temperature (T) in Kelvin and kinetic energy (KE) is given by: KE∝T

This relationship highlights that temperature is a measure of the average kinetic energy per particle.

Conclusion: According to the kinetic theory, heat is associated with the kinetic energy of particles, and temperature is a measure of the average kinetic energy per particle. The theory provides a microscopic perspective on the thermal behavior of matter.

SECTION-D

Note: Long answer type questions. Attempt any two questions out of three questions. (2x8=16)

Q.23 Explain Newton’s First Law, Second Law, and Third Law with examples.

Ans: Sir Isaac Newton's three laws of motion describe the relationship between the motion of an object and the forces acting on it.

1. Newton's First Law (Law of Inertia):

• Statement: An object at rest will stay at rest unless a net external force appllied. An object in motion will stay in motion with a constant velocity unless a net external force is applied.

• Explanation: This law highlights the concept of inertia. Inertia is the tendency of an object to resist changes in its state of motion. In the absence of external forces, an object will maintain its current state of motion.

• Example: If you slide a book on a frictionless surface, it will keep sliding indefinitely if no external force (like friction) acts upon it.

2. Newton's Second Law:

• Statement: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law is often expressed by the equation

• F=ma,

• · F is the net force applied to an object,

• · m is its mass,

• · a is the resulting acceleration.

• Explanation: This law tells the relationship between the force applied to an object and the resulting motion. The greater the force applied to an object, the greater its acceleration will be. Similarly, a larger mass will result in less acceleration for the same force.

• Example: If you push a shopping cart with a certain force, it will accelerate more if it's empty (less mass) compared to when it's full of groceries (more mass).

3. Newton's Third Law:

• Statement: For every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

• Explanation: This law highlights the symmetry of forces in nature. Forces always occur in pairs. The two forces are equal in magnitude but act in opposite directions.

• Example: Jump off a diving board, the body exerts a downward force on the board. The board simultaneously exerts an equal and opposite upward force on the body to push the body into the air

Q.24 a) Explain systems of units.

Ans: Systems of units are standardized sets of units for expressing measurements. These systems provide a reliable and logical. These measurements are universally understood. There are two types of systems of units. These are the International System of Units (SI) and the Imperial.

1. International System of Units (SI):

• Base Units:

  • · Meter (m) for length

  • · Kilogram (kg) for mass

  • · Second (s) for time

  • · Ampere (A) for electric current

  • · Kelvin (K) for temperature

  • · Mole (mol) for the amount of substance

  • · Candela (cd) for luminous intensity

Derived Units: These are combinations of base units to express other quantities. For example, the unit for speed is meters per second (m/s), which is a derived unit.

Prefixes: SI uses prefixes to denote decimal multiples or submultiples of units. For example, a kilometer (km) is a thousand meters, and a millisecond (ms) is one-thousandth of a second.

• 2. Imperial and U.S. Customary Systems:

  • Length:: Inch (in), foot (ft), yard (yd), mile (mi)

  • Mass: Ounce (oz), pound (lb), ton (short ton or long ton)

  • Time: Second (s), minute (min), hour (h).

  • Volume: Fluid ounce (fl oz), cup, pint, quart, gallon.

  • Temperature: Fahrenheit (°F) in the U.S. Customary System, but Celsius (°C) is also used in some contexts.

  • Force: Pound-force (lbf),

  • Energy: British thermal unit (BTU),

  • Pressure: Pound-force per square inch (psi)

The SI system is widely used in scientific and most international contexts. The Imperial and U.S. Customary Systems are more common in the United States and some other countries. The adoption of the SI system is increasing globally in scientific and engineering fields.

It's important to note that using consistent systems of units is crucial to avoid errors and misunderstandings in measurements and calculations. Scientists, engineers, and professionals across different disciplines adhere to specific unit systems to ensure accurate and standardized communication.

b) Convert the force of 20 Newton into dyne.

Ans: A dyne is a unit of force in the centimeter-gram-second (CGS) system. 1 Newton is equal to 100,000 dynes.

To convert 20 Newtons to dynes:

• Force in dynes = Force in Newtons × Conversion Factor.

• Force in dynes = 20 N × 100,000 dynes/N

• Force in dynes = 2,000,000 dynes

So, 20 Newtons is equal to 2,000,000 dynes

Q.25 Explain Conduction, Convection, and Radiation with examples.

Ans: Conduction, convection, and radiation are three primary mechanisms of heat transfer. Each occurs in different ways

1. Conduction:

• Definition: Conduction is the process of heat transfer through direct contact between particles of a substance. It occurs in solids, where the particles are closely packed together.

• Example: Heating one end of a metal rod, the particles at that end gain energy and vibrate. These vibrations are then passed on to adjacent particles, and this continues throughout the rod. This leads to the transfer of heat from one end to the other

2. Convection:

• Definition: Convection is the process of heat transfer through the movement of fluids (liquids or gases). It involves the transfer of heat by the actual movement of the heated fluid from one place to another.

• Example: Boiling water is a classic example of convection. As water is heated, the molecules near the heat source become energized and move upward. Cooler, denser water then moves downward to replace it. This creates a circular flow of water, transferring heat throughout the entire container

3. Radiation:

• Definition: Radiation is the transfer of heat through electromagnetic waves. Unlike conduction and convection, radiation does not require a medium and can occur in a vacuum.

• Example: The sun's energy reaching the Earth is a form of radiation. The sun emits electromagnetic waves (including visible light) that travel through the vacuum of space and reach the Earth. Another example is the heat you feel when sitting close to a fire or a hot object without direct contact.

Conclusion:

• Conduction involves the transfer of heat through direct contact with solids.

• Convection involves the transfer of heat through the movement of fluids.

• Radiation involves the transfer of heat through electromagnetic waves and can occur in a vacuum.

Dr Pramila Singh