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Concept:

• The time period of the simple pendulum is given by, \(T=2\pi √{\frac{l}{g}} \), Where, l =  length of the string, T = time period, g = acceleration due to gravity.
• The acceleration on the moon is one-sixth of the acceleration due to gravity on the earth.
• The time period of the pendulum is inversely proportional to the acceleration due to gravity, \(T\propto \frac{1}{√{g}}\)

Explanation:

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

From the above expression, the time period of the pendulum is inversely proportional to the acceleration due to gravity,

\(T\propto \frac{1}{√{g}}\)

We know that the acceleration on the moon's surface is one-sixth of the acceleration due to gravity on the earth.

\(g'=\frac{g}{6} \)

\(\frac{T}{T'}= √\frac{\frac{g}{6}}{{g}} \)

\(\frac{T}{T'}= √\frac16\)

T' √6 T 

So, when the pendulum is taken on the moon the value of g will decrease. Hence, the pendulum takes more time to complete one vibration. It will become slow.

Concept:

• Bats detect obstacles in their flying path by a process called echolocation.
• Echolocation: It is a Phsicilgical process for locating distant objects or obstacles by sound waves reflected back to the emitter.
• The bats emit Ultrasonic waves in the echolocation process.
• The frequency range of the Ultrasonic wave is 20 kHz to 200 kHz.

Explanation:

• Baths detect obstacles in their flying path by a process called echolocation.
• In this process, a bat emits ultrasonic waves of frequency range 20 kHz to 200 kHz.
• If there are any obstacles in their path, these waves strike and bounce back, sending them back to the bat.
• Then, the bat process this information to determine the size of the object and how far it is.

Concept:

• During the day the sun heats up the earth's surface, warming the air close to the ground.
• Sound travels faster in warmer air. So the sound travels faster in the air close to the ground.
• The reverse happens at night.
• The speed of the sound in air is given by, \(v=\sqrt{\frac{γ RT}{M}}\) where M = molecular mass of the air, R = Universal gas constant, T = temperature, γ = adiabatic index
• In terms of density, speed, \(v=\sqrt{\frac{β}{ρ}}\), where β = bulk modulus, ρ = density

Explanation:

The speed of the sound in air is given by, \(v=\sqrt{\frac{γ RT}{M}}\)

In terms of density and bulk modulus, \(v=\sqrt{\frac{β}{ρ}}\) 

From the above expression, the speed of the sound is depended on the following factors,

• The temperature
• density: The composition of the air and the humidity(moisture) change the density
• The speed is almost independent of the atmospheric pressure.

Concept: 

• All mechanical waves that occur in nature are called Sound waves.
• The sound wave cannot travel in a vacuum.
• The SI unit of the sound is Decibel
• The speed of the sound in air is, \(v=\sqrt{\frac{\gamma RT}{M}}\) where, M = molecular mass of the air, R = Universal gas constant,  T =  temperature
• Intensity formula, \(I(dB)= 10 log _{10} (\frac{I}{I_0})\)
• The Decibel is used to measure the intensity of sound.

Additional Information

• Magnetic field

• A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

• The SI unit of the magnetic field is Tesla, denoted by the capital T.

• Light

• Light is a form of energy that makes us see.

• The intensity of the light can be measured with the help of a photometer.

• The speed of light in the air is 3 ×10⁸ m/s

• Heat

• ​​Heat is a form of energy that produces the sensation of warmth.

• Its SI unit is Joule,

• The heat flows from a higher-temperature body to lower temperature body.

Concept:

• capacitor, a device for storing electrical energy, consisting of two conductors in close proximity and insulated from each other.
• It is used to store the energy in presence of an electric field.
• It is a device used to store an electric charge between two plates.
• It consists of one or more pairs of conductors separated by an insulator.
• The SI unit of capacitance is Farads (F).

Explanation:

A capacitor is used in our TV set, computer, and radio set for storing the electric charge.

Hence, the correct option is 3.

Additional Information

• Inductor
• ​A component in an electric circuit that possesses an inductance.
• A two-terminal passive component, store energy in a magnetic field.
• Resistor​​​​
• A device having resistance to the passage of electric current.
• The SI unit of resistance is the ohm.
• Conductor
• A material that conducts heat and electricity through it is called a conductor.
• For example, Silver, aluminum,

Concept:

• Electric charge: It is an intrinsic property of the elementary particle of matter which gives rise to electric force between various objects.
• It is a scalar quantity.
• The total charge on the conductor is given by, q = It, when an electric current is flowing in the conductor for some time.
• Here, I = Electric current, t = time
• The SI unit of electric charge is Coulomb denoted by C.

Explanation:

• When a soap bubble is charged, an electric charge particle will be distributed over the surface of the soap bubbles.
• It expands to decrease the surface tension or minimize the surface tension.
• The soap bubble is expanded means an increase in size, so its radius also increases.

Concept:

Capacitance

• Capacitance is a property of the electric conductor measured by the amount of separated electric charge that can be stored on it per unit change in electrical potential.
• In capacitor, amount of charge, Q = CV, where, C = Capacitance, V = electrical potential
• A capacitance in an electric circuit is introduced by a device called a capacitor.
• The SI unit of the capacitance is Farad and is denoted by the F.

Explanation:

The SI unit of capacitance is Farad denoted by F.

Additional Information

• Resistance
• ​​Resistance in an electric circuit is introduced by a device called a resistor.
• Formula, V = IR, where I = electric current flowing in the circuit, V =  supplied voltage, R = Resistance
• The SI unit of resistance is Ohm denoted by Ω.
• Conductance
• ​The reciprocal of the resistance In a conductor is called conductance.
• Relation, \(Conductance=\frac{1}{Resistance}\)
• The SI unit of conductance is Ohm^-1.
• Inductance
• ​The inductance in an electric circuit is introduced by a device called an inductor.
• The SI unit of the inductance is Henery denoted by H.

Concept:

• Gravitational Force:
• ​It is the force responsible for holding planets in their orbits and this is possible only because of their infinitely long range.
• It is the weakest force.
• It is also the attractive force that arises from the gravitational interaction.
• ​Coulomb Force:
• ​An electrostatic force is also known as the Coulombic force.
• It is the force of attraction between two opposing charges, i.e., protons and electrons.

Explanation:

• The dominating force in the universe is the gravitational force, not a coulomb force because the gravitational force is applied on the macroscopic level, between stars or planets.
• The gravitational force is weaker than the coulomb force.

Hence, the assertion and reason both are incorrect.

Additional Information

• Nuclear strong force:
• The nuclear force is a force that acts between the protons and neutrons of atoms.
• This force can exist between protons and protons, neutrons and protons, or neutrons and neutrons.
• The nuclear force is the force that binds the protons and neutrons in a nucleus together.
• This force is what holds the nucleus together.
• ​Weak force:
• ​The weak force is the force existing between the elementary particles which are responsible for certain processes to take place at a low probability.
• The Weak nuclear force is responsible for the change in quark into other forms.

Concept:

• A comb moving through dry hair gets electrically charged through induction.
• Induction charging is a charging method that charges an object without actually touching the object to any other charged object.
• The charging by induction process is where the charged particle is held near an uncharged conductive material that is grounded on a neutrally charged material.

Explanation:

• When a comb is moved through dry air, charge transfer takes place between the comb and hair and so the comb becomes electrically charged.
• Electric field lines of force always originate at the positive charge and terminate at the negative charge.
• So, they do not form a closed loop.
• Whereas the magnetic field lines of force always form a closed loop.

Hence, both statements are correct.

Concept:

• Conducting sphere can be electrically charged through induction.

• Induction charging is a charging method that charges an object without actually touching the object to any other charged object.

• The charging by induction process is where the charged particle is held near an uncharged conductive material that is grounded on a neutrally charged material.

• Charge:

• ​It is the property of matter that is responsible for the electrical phenomenon.

• Two- types: Positive charge and negative charge.

• Law of conservation of charge:

• ​The charge can neither be created nor destroyed.

• It can be only transferred from one system to another system.

Explanation:

• If two conducting spheres are separately charged and then brought in contact.
• Then, the total charge on the two-sphere is conserved by the law of conservation of charge.
• But, energy may not conserved because of the different sizes or having different charges then some of the energy might losses in the distribution of the charge.
• In the case of final potential, the final potential is not always the mean of the original potential of the two spheres because of the distribution of the charge and some losses occur but, the final potential of both spheres is equal.