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Concept:

Work:

• ​Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
• Formula, W = F× d, where F = component of force, d = magnitude of the displacement, W =  work done
• The SI unit of the work is Joule or N-m.
• The dimensional formula of the work, [W] = [M¹L²T^-2].

​Energy:

• It is defined as the ability to do work.
• The SI unit of the energy is Joule.
• The dimensional formula of the energy, [E] = [M1L2T-2].

​Explanation:

The dimensional formula of the energy and work is the same.

[W] = [E] = [M1L2T-2].

Additional Information 

Power: 

• Power is the amount of energy transferred or converted per unit of time.
• Formula, \(P=\frac{E}{t}\), where P = power, E = energy transferred, t = time.
• The SI unit of the power is Joule/s.
• The dimensional formula of the power,  [W] = [M1L2T-3].

Force:

• ​Force is defined as the product of mass and acceleration.
• It is a vector quantity because it has both magnitude and direction.
• Formula, F =  ma, where, F = force, m = mass, a = acceleration
• The SI unit of force is N or kg ms^-2.
• The dimensional formula of the force, [F] = [M¹L¹T^-2]

Momentum:

• ​Momentum is defined as the product of the mass and velocity of an object.
• It is a vector quantity because it has both magnitude and direction.
• Formula, P = mv, where m = mass of the object, v = velocity, P = momentum
• The SI unit of momentum is kg ms^-1.
• The dimensional formula of the momentum is [P] = [M¹L¹T^-1].

Concept:

• Acceleration: It is defined as the rate of change of velocity with respect to time.
• It is a vector quantity because it has both magnitude and direction.
• The SI unit of acceleration is ms^-2.

Explanation:

• A passenger in a moving train tosses a five rupees coin.
• The coin has the same velocity as the velocity of the train, but during the time, the coin is in the air, the train keeps moving forward and the coin falls behind the passenger.
• Hence, the train must be moving with uniform acceleration.

Additional Information

Deceleration:

• ​​When the velocity of the body decreases with time, then the acceleration becomes negative.
• The negative acceleration is also known as deceleration or retardation.

Velocity:

• ​It is defined as the rate of change of displacement with respect to time.
• It is a vector quantity because it has both magnitude and direction.
• The SI unit velocity is ms^-1.

Speed:

• ​It is defined as the rate of change of distance with respect to time.
• It is a scalar quantity because it has only magnitude but not direction.
• The SI unit velocity is ms-1.

Concept:

Newton's First Law of motion

• This law implies that things cannot start, stop, or change direction all by themself, it requires some external force.
• ​It states that a body that is at rest or uniform motion will continue to be at rest or uniform motion until or unless a net external force is applied to it.
• It is also known as the law of inertia.

Additional Information

Newton's second law of motion

• ​It describes what happened to the massive body when acted upon by an external force.
• This law states that the net external force acting on the object is equal to the product of mass and acceleration.
• Formula, F = ma, where, m = mass, a = acceleration

Newton's third law of motion

• It describes what happened to the body when it exerts a force on another body.
• ​This law states that there is an equal and opposite reaction for every action.

Concept:

Potential energy

• It is the energy possessed due to the position of the object is called potential energy
• The potential energy due to gravitation, P.E = mgh, where m = mass, g = acceleration due to gravity, h = height
• Potential energy due to spring, \(P.E=\frac{1}{2}kx^2\), where k = spring constant, x = displacement
• In the case of spring, the potential energy increases when a spring is stretched or squeezed.

Explanation:

• In the case of the spring, the potential energy increases when a spring is stretched or squeezed.
• Work is done against the gravitational force of attraction when moving a body against gravity. It indicated that the potential energy of the system has increased.
• When the bubble rises in the direction of the upthrust force, the potential energy of the system gets vanished.

Hence, the correct option is 2.

Additional Information

• Kinetic energy
• The energy possessed due to the motion of an object is called kinetic energy.
• Formula, \(K.E=\frac{1}{2}mv^2\), where m = mass, v =v velocity

Concept:

• The acceleration due to gravity on the earth's surface, \(g=\frac{GM}{R^2}\) where, G = universal gravitational constant, M = mass of the earth, and R =  radius of the earth.

• We know that Re > R_p, where Re =  radius of the earth on the equator side, R_p = radius of the earth on the pole side.

• The acceleration due to gravity is inversely proportional to the square of the radius of the earth.

• Relation, \(g\propto \frac{1}{R^2}\)

• In case of rotation. \(g'=g(1-Rω^2cos^2\phi)\), where, R = radius of the earth, ω = angular velocity of the earth.

• g is decreasing at the earth's surface than at a height above or at a depth below it.

Explanation:

• The acceleration due to gravity is not the same at all places on the surface of the earth due to the elliptical size of the earth.
• The acceleration due to gravity at the equator is less than that of a pole.
• That means g is greater at the poles than at the equator.
• At the equator, θ = 0º \()the value of g is minimum.
• At the pole, θ = 90º, the value of g is maximum.
• g decreases at the earth's surface than at a height above or at a depth below it.

Concept:

Young's modulus of elasticity 

• It is defined as the ratio of normal stress to the longitudinal strain within the elastic limit.
• \(Y=\frac{\sigma}{\epsilon}\)
• It represents the longitudinal elasticity.
• Formula, \(Y=\frac{F/A}{Δ l/l}\) where, F =  force, A = area, Δl = change in length, l = original length

The bulk modulus of elasticity

• ​ It is defined as the ratio of normal stress to the volumetric strain, within the elastic limit.
• It represents the volumetric elasticity.
• Formula, \(K=-\frac{P}{\Delta V/V}\) where, P = pressure, Δ V =  change in volume, V =  volume

Additional Information

• Shear modulus of elasticity
• It is defined as the ratio of shear stress to shear strain.​
• Shear modulus, also known as Modulus of rigidity.

Concept:

Joule-Thomson effect: 

• The Joule-Thomson effect also known as Kelvin–Joule effect or Joule-Kelvin effect is the change in fluid’s temperature as it flows from a higher pressure region to lower pressure.
• The basic principle of the Joule-Thomson effect is based on the transfer of heat.
• The cooling produced in the Joule-Thomson expansion has made it a very valuable tool in refrigeration.

Explanation:

• When a puncture happens, the air flows from the high-pressure region inside to the low-pressure region outside.
• As air gains kinetic energy, it gains this energy from the internal heat of the air.
• So it will use the internal energy of the compressed air, so it uses up internal heat and temperature falls.
• This phenomenon is referred to as, the Joule-Thomson effect.

Concept:

Specific heat at constant pressure

• ​If the heat transfer to the sample is done when it is held at constant pressure.
• Then the specific heat obtain using such a method is called Molar Specific Heat Capacity at Constant Pressure.
• It is denoted by C_P.

Specific heat at constant volume

• ​If the heat transfer to the sample is done when the volume of the sample is held constant.
• Then the specific heat obtain using such a method is called Molar Specific Heat Capacity at Constant Volume.
• It is denoted by C_V.
• Work done in thermodynamics is given by, W = PΔV
• At constant pressure, work is done in the expansion of gas.
• At constant volume, there is no work done in the gas expansion. Or simply means, work done is zero.

Explanation:

• When a gas is heated at constant volume, the whole heat supplied to the gas is used up in raising its temperature.

• When a gas is heated at constant pressure, the gas is allowed to expand under constant pressure, heat supplied is used up in raising the temperature as well as in doing external work against expansion.

• Therefore, the specific heat of a gas at constant pressure is greater than the specific heat at constant volume.

• The specific heat of a gas at constant pressure is greater than the specific heat at constant volume because work is done in the expansion of the gas at constant pressure.

Hence, the correct option is 2.

Concept:

• The time period of the pendulum is given by, \(T=2\pi \sqrt{\frac{l}{g}}\) where g = acceleration due to gravity, l = length of the rod.
• The time period of the pendulum is directly proportional to the square root of the length of the rod.
• Relation, \(T\propto\sqrt{l}\)
• The SI unit of time period is second.

Explanation:

The time period of the pendulum is given by, \(T=2\pi \sqrt{\frac{l}{g}}\)

From the above expression, the time period of the pendulum is directly proportional to the square root of the length of the rod.

• For speeding up, in a pendulum clock, the time period should be decreased.
• and it can be achieved by reducing the length of the rod.
• Hence, the slow-running pendulum clock can be speeded up by reducing the length of the rod.

Concept:

• The basic properties of the waves are wavelength, frequency, velocity, and amplitude.

• Wavelength is defined as the distance between the crest or troughs of a wave motion.

• Frequency is defined as the number of oscillations per unit of time.

• The relation between the frequency, wavelength, and velocity is given by, v =  fλ  where v = velocity,  f = frequency, λ = wavelength

• The velocity of the sound in a solid, \(v=\sqrt{\frac{β}{ρ}}\) where, β = bulk modulus, ρ = density

Explanation:

• When a sound goes from one medium to another medium, the wavelength changes but the frequency remains the same because the frequency of the sound depends on the source of the sound.
• The relation between the frequency, wavelength, and velocity is given by, v =  fλ, where v = velocity,  f = frequency, λ = wavelength
• The velocity of the sound depends on the elasticity and the inertia of the medium. Hence, the velocity also changes when the sound wave goes from one medium to another medium.
• When a particle moves from one medium to another medium, its amplitude increases or decreases depending on the medium.

Hence, when a wave goes from one level to another, there is a change in amplitude, velocity, and wavelength, but the frequency of sound remains constant.

Important PointsThe given question in Official paper is 

When a wave goes from one level to another, there is change in the ___. 

Which is found to be wrong. therefore we corrected the question and modified it.