MPTET Varg 1 Physics Mock Test - 2 - MPTET MCQ

दिए गए विकल्पों में से "भर्ता" शब्द 'पति' का पर्यायवाची है।
पति के अन्य पर्यायवाची शब्द - स्वामी, प्राणाधार, प्राणप्रिय, प्राणेश, आर्यपुत्र, दूल्हा, वल्लभ, भर्तार, सुहाग, सौहर, साजन, बालम, वर।
स्पष्टीकरण
अन्य विकल्प:

• विधाता के पर्यायवाची शब्द - ब्रह्मा, विधि, सृष्टिकर्त्ता।
• विभु के पर्यायवाची शब्द - सर्वव्यापक, नित्य, अनन्त, अजन्मा।
• भार्या के पर्यायवाची शब्द - प्रिया , अंगना , पत्नी , प्रणयिनी , प्रेमिका , स्त्री , वामा।

अन्यसंबंधित बिंदु
पर्यायवाची शब्द:
सामान्य अर्थ में ऐसे शब्द जिनके अर्थ समान हों, पर्यायवाची शब्द कहलाते हैं।
पर्यायवाची शब्द के कुछ उदाहरण :

• अतिथि- मेहमान ,पाहुन ,आगंतुक, अभ्यागत।
• इज्जत– मान, प्रतिष्ठा, आदर, आबरू।
• उपहास– परिहास, मजाक, खिल्ली।
• एकांत – निर्जन सुनसान शून्य।
• औषधि- दवा, दवाई, भेषज।
• किरण- अंशु, रश्मि, कला, कर, गो, प्रभा, दीधिति, मयूख, मरीचि।
• कंठ- गला, शिरोधरा, ग्रीवा, गर्दन।
• गाय- भद्रा, गौरी, सुरभी, धेनु, गऊ, गौ,गैया, पयसि्वनी,दोग्धी।
• घी- हव्य, अमृतसार, क्षीरसार, आज्य।
• चर्म- खाल, चमड़ी, त्वचा, त्वक्।
• छाछ- गोरस, मठा, दधि स्वेद, मट्ठा।
• झंडा- पताका, केतु, निसान, ध्वज, केतन, वैजयंती।

'उत्तराधिकार में प्राप्त सम्पत्ति - इन अनेक शब्दों के लिए एक शब्द है- 'रिक्थ'
गलतीअंक

• वह गुण, वस्तु या विचार जो परम्परा के रूप में हमें पूर्वजों से मिला हो - धरोहर
• किसी की मृत्यु के बाद उसकी सम्पत्ति पाने का अधिकार - उत्तराधिकृत
• वह मूल्यवान वस्तु जिस पर किसी का अधिकार हो - परिसम्पत्ति

स्पष्टीकरण

• अनेक शब्दों के लिए एक शब्द को प्रयुक्त करना ही वाक्यांश के लिए एक शब्द कहलाता है।

अन्यसंबंधित बिंदु
कुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द:-

• जिस पर मुकदमा चल रहा हो - अभियुक्त
• किसी एक में ही आस्था रखने वाला - अनन्य
• वह चीज जिसकी चाहत हो - इच्छित
• जिसके ऊपर किसी का उपकार हो - उपकृत
• जो इन्द्रियों से संबंधित हो - ऐन्द्रिय
• जिसकी बुद्धि बहुत तेज हो - कुशाग्र
• जिसका कुछ ही समय में नाश हो जाए - क्षणभंगुर
• जो दूसरों में केवल दोषों को ही खोजता हो - छिद्रान्वेषी

सही उत्तर है - कृपा करना, दया करना, मानसिक पीड़ा, शारीरिक रोग
स्पष्टीकरण

• अनुग्रह -कृपा; प्रसाद। ईश्वरीय कृपा। राज्य की कृपा से प्राप्त सहायता या सुविधा।
• आधि- अभाव जनित रोग, मानसिक स्थिति की नकारात्मक छवि। व्याधि- शारिरिक कष्ट, वात, पित्त, और कफ की स्थिति।

महत्वपूर्णबिंदु

• भिन्नार्थक शब्द: जो शब्द सुनने में एक जैसे लगते हैं लेकिन उनका अर्थ अलग होता है उन्हें भिन्नार्थक शब्द कहते हैं।
• इन्हे श्रुतिसम भिन्नार्थक या शब्द युग्म भी कहते हैं।

अन्यसंबंधित बिंदु
पर्यायवाची शब्द

• जो शब्द समान अर्थ के कारण किसी दूसरे शब्द की जगह ले लेते हैं उन्हें पर्यायवाची शब्द कहते हैं
• या समान अर्थ प्रदान करने वाले शब्द पर्यायवाची शब्द अथवा समानार्थक शब्द कहलाते हैं।

समानार्थी

• समानार्थी का अर्थ होता हैं (सामान + अर्थ) अर्थात किसी शब्द का सामान अर्थ वाले दूसरे शब्द या उसी के सामान कोई दूसरा नाम (वस्तु)।
• “वे शब्द जिनका अर्थ एक समान होता हैं समानार्थी शब्द कहलाते हैं समानार्थी शब्द को हम पर्यायवाची शब्द भी कहते है।

सही उत्तर पंखे है।
स्पष्टीकरण

• दिए गए सभी शब्दों में से 'पंखा' का बहुवचन शब्द 'पंखे' होगा।
• पंखा का अर्थ- बिजली से चलने वाला वह यंत्र जो हवा देता है।

अन्यसंबंधित बिंदु

The correct answer is 'woe'.

Explanation

• Jubilation: A feeling of great happiness, especially because of a success
  • ​E.g.- The news was greeted with jubilation.
• Woe: A strong feeling of sadness
  • ​​E.g.- The city's traffic woes are well-known.

Hence, the correct answer is 'woe'.

Other Related Points

• Happiness: The feeling of being happy
  • ​​E.g.- It was only later in life that she found happiness and peace of mind.
• Festivity: The parties, meals, and other social activities with which people celebrate a special occasion
  • ​​E.g.- Come in and join the festivities!​
• ​Triumph: A great success or victory; the feeling of happiness that you have because of this
  • ​​​E.g.- The team returned home in triumph.

The correct solution is '13542'.
Explanation

• While arranging a jumbled sentence, we have to analyze all our options carefully, find a common theme and arrange them accordingly.
• Looking ath the options given above, we can kniw that the sentence given are trying to talk about 'gum disease'.
• Option 1, ' People with severe gum disease are almost twice as likely to suffer from a heart attack or stroke' is the first sentence as it introduces us to the commoness of a gum disease.
• Option 3, 'But researchers are still trying to find out if there is a cause-and-effect relationship'. comes next as it explains the problem with the disease.
• Option 5, ' Even those with moderate gum problems have a higher rate of circulatory problems' comes next as it continues to explain the problem nwith the disease.
• Option 4, ' Why this happens is yet unknown' is the next sentence as it talks about the dead end with finding the cause of the disease.
• Option 2, ' However, one recent Belgian study found that when people with gum disease chewed food, bacteria were released into their bloodstream that could increase inflammation' end the passage as this sentence gives explains the only discover regarding the disease.
• Hence the correct solution is Option 4.

The erroneous part is 'Each of the students were'.
Explanation

• The given sentence is grammatically incorrect.
• Here, 'Each of the students was' should be used instead of 'Each of the students were'.
• We know when a sentence starts with 'Each of' its structure should be:
• Each of + Plural Noun/Pronoun + Singular Verb.
• Example:
  • Each of the survivors of the capsized ship has told the same story.
  • Each of the survivors of the capsized ship have told the same story.

• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.

Correct Sentence: Each of the students was present for the valedictory session that night.

Bhakra Nangal Project is the biggest multipurpose river valley project in India.

Explanation

• The Bhakra Nangal Dam is a concrete gravity dam in India.
• It is located near the border between Punjab and Himachal Pradesh in the northern part of the country.
• Situated across the Sutlej River, this dam is said to be the second-tallest dam in Asia, with a height of 740 ft.
• It is the biggest multipurpose river valley project in India.
• One of the primary uses of this dam is storing rainwater for irrigation purposes.
• The water of the dam helps in providing electricity to many areas of the states of Himachal Pradesh, Chandigarh, Haryana, Rajasthan, Punjab, and Delhi.
• It is a popular tourist destination that was called the ‘New Temple of Resurgent India’ by the country’s first prime minister, Jawaharlal Nehru.

• The reservoir of this dam is called the ‘Gobind Sagar’.

The correct answer is Karnataka.

Explanation

• In the BCCI Under-19 women's cricket tournament played in Ahmedabad, Madhya Pradesh won the championship by defeating Karnataka.
  • Madhya Pradesh defeated Karnataka by 26 runs in the final played in Ahmedabad.

Other Related Points

• Earlier, Madhya Pradesh had made it to the final by defeating Delhi in the semi-finals.
• For Madhya Pradesh, opener Kanishk Thakur scored 52 runs in 60 balls with the help of four fours.
• The Directorate of Sports and Youth Welfare is a department of the state government of Madhya Pradesh is responsible for development in the field of sports and youth welfare.
• Madhya Pradesh Cricket Association (MPCA) is one of the major cricket governing provincial units affiliated to the Board of Control for Cricket in India (BCCI). MPCA is a regular participant in all domestic tournaments organized by BCCI.

Piaget and Vygotsky proposed theory regarding the role of language for development and the relationship between language and thought.

• According to Piaget, thought comes before language, which is only one of its forms of expression. The formation of thought basically depends on the coordination of sensory-motor schemes and not of language. This can occur only after the child has reached a certain level of mental abilities, subordinating herself, to the thought processes. The language allows the child to evoke an object or event absent at the communication of concepts.
• Piaget insists that the language and thought of the child are aspects of cognitive processes. The intellectual development of the child can be understood through his/her language and thought processes.
• Piaget primarily concentrated on the cognitive aspect, another dimension was added by Vygotsky
• According to Vygotsky, thought and language is interdependent processes, from the beginning of life. The acquisition of language by the child modifies its higher mental functions: it gives a definite shape to thought, enables the emergence of imagination, memory usage, and action planning.
• All fundamental cognitive activities including language take place in a matrix of social history. He believed that cognitive skills and patterns of thinking are not determined by innate factors but are the product of the interaction between the individual and the socio-cultural institution where the individual grows up.

Hence, from the above point it is clear that according to Piaget, a thought emerges first and according to Vygotsky, language has a profound effect on thought.

A school curriculum is a complete set of organized experiences in the school. It includes aims, objectives, teaching content, teaching strategies, and all teaching-learning aids to cater totality of student's experiences that occur in the educational process.

Explanation

The sequential order of curriculum development:

• Assessment of needs: In this process, the teacher assesses students regularly to check and report on their progress and make decisions about further teaching. Therefore it is important that a teacher adopts a responsible and sensitive approach towards assessment.

• Formulation of objectives: After assessing the needs or requirement area, the next of developing a curriculum is to formulate the objectives as per the student's learning needs. Those objectives should be formulated which would be achieved at the end of the course.

• Selection of texts/learning experiences: Selection of learning resources is a very important and crucial step for developing a curriculum. The learning resources should be as per the needs and desires of the learning. It should be complementary in achieving formulated learning objectives. It should give direct experience to the learner and makes the learning more effective.

• Evaluation of the curriculum: Evaluation procedures to be done to check the results of the curriculum after the implementation. Through this, the school administration will get the optimum feedback on what should be added and what should be removed from the curriculum to make it more significant.

Other Related Points

Salient features of curriculum:

• Makes learning an integrated process.
• Nurtures learner's holistic development.
• Introduces structure of program of study.
• Improves totality of student's experience.
• Includes teaching strategies and contents.
• Promotes inclusive education to all learners.
• Provides ample opportunities for all-round development.

Hence, it could be concluded that assessment of needs, formulation of objectives, selection of texts/learning experiences, evaluation is the sequential order of curriculum development.

Learning Disability is a neurological disorder that affects the way one receives and processes information. There are various types of learning disabilities in children.

Explanation

• Dyspraxia is a developmental disorder of the brain in childhood causing difficulty in muscle control as well as activities requiring coordination and movement.
• This motor skill development is a type of learning disability specifically related to motor skills.
• It is also known as developmental coordination disorder or motor learning disability.
• Children with dyspraxia struggle with coordination and movement.

Hence, it can be inferred that a disorder characterized by problems with movement and motor skill coordination is Dyspraxia.

Concept:

For a translational motion force causes the particle to accelerate in a straight line and similar to this for rotational motion the coupled forces (equal and opposite forces) causes any particle to rotate along some axis of rotation as shown below and this coupled force is known as Torque or Moment of force.

Thus, torque is a type of force that can cause an object to rotate along some axis of rotation.

And it can be given as

Torque,

⇒

Here τ is the torque acting on an object whereas r is the distance between forces or axis of rotation and θ is angel between r and F

Application:

• If the doors are provided with handles near the outer edges away from the hinges the force or the distance between the axes of rotation will increase.
• As the distance value increased, the torque also increased, so to apply maximum torque to the door.
• Hence, doors are provided with handles near the outer edges for easy opening.

Concept:

• Pascal is a unit of pressure which is defined as the force per unit area.
• The formula for the coefficient of the viscosity, , where, F= force, d= distance between the layers, A= cross-sectional area, v= velocity
• The time can be written in terms of velocity and distance as,

Explanation:

Pascal is a unit of pressure which is defined as the force per unit area.

The SI unit of pressure-Time is . . . . . . . . .(1)

The formula for the coefficient of the viscosity,

where, F= force, d= distance between the layers, A= cross-sectional area, v= velocity

The SI unit of the coefficient of the viscosity is . . . . . . . . (2)

where, F= force, d= distance between the layers, A= cross-sectional area, v= velocity

From equation (1) and equation (2), we can conclude,

the dimension formula of the pascal-second is equal to the dimensional formula of the coefficient of viscosity.

Other Related Points

• The dimensional formula of the force,
• The dimensional formula of the energy,
• The dimensioal formula of the pressure,

CONCEPT:
The potential difference across the capacitor is written as;

V_rms is the potential difference in root mean square.
CALCULATION:
Given: V_rms = 220 V
As we know,

⇒
Hence, option (4) is the correct answer.

Concept:

Three equations of motion are:

v = u + at

v²-u²=2as

s= ut+ 1/2 (at²)

where u and v are initial and final velocities respectively, t is time, s is distance travelled, a is acceleration.

Calculation:

Initial velocity of car = 0

Acceleration of car = 5 m/s²

Velocity of car at t = 4 s; v = u + at

⇒ v = 0 + 5 × 4 = 20 ms^-1

At t = 4 s, A ball is dropped out of a window so velocity of ball at this instant is 20 ms^-1 along horizontal.

After 2 seconds of motion

Horizontal velocity of ball = 20 ms^-1 (∵ a_x = 0)

Vertical velocity of ball (V_y) = u_y + a_yt

v_y = 0 + 10 × 2 = 20 ms^-1 (∵ a_y = g = 10 m/s²)

So magnitude of velocity of ball

m/s

Acceleration of ball at t = 6 s is g = 10 m/s²

As ball is under free fall.

The correct answer is option 1) i.e. Each point in a wavefront is a source of secondary waves.
Concept:
Huygens' concepts of secondary wavelets:

• Huygen’s principle states that every point on the wavefront may be considered as a source of secondary spherical wavelets that spread out in the forward direction at the speed of light.
  • The new wavefront is the tangential surface of all these secondary wavelets.
  • Secondary sources start making their own wavelets, these waves are similar to that of the primary source
  • It states that each point on a wavefront is a source of wavelets, which spread forward with the same speed.

• Wavefront: A wavefront is a surface or a line on which the disturbance at every point has the same phase.
• Wavelets: It is a wave-like oscillation with an amplitude that starts at zero, increases, and then decreases back to zero.

Explanation:

• Huygens's principle states that each point on a wavefront is a source of wavelets, which spread forward with the same speed.

Concept:-
Force:-

• Force is an external cause that is capable of changing the state of rest or motion of a particular object.
• Force is a vector quantity. So it has both magnitude and direction.
• The direction along which a force is applied is known as the direction of the force and the point where force is applied is called the application point.
• Usually, the magnitude of Force is measured by using a spring balance.
• The SI unit of force is Newton (N).
• The physical quantity force is quantified by the product of mass (m) with acceleration (a).
• The force can mathematically be expressed as:-

F = ma
Where,
m = mass
a = acceleration
It is articulated in Newton (N) or Kg m/s2.
Calculation:-
The parallelogram law:-

• When two vectors are acting simultaneously at a point, then it can be represented both in magnitude and direction by the adjacent sides drawn from a point.
• So, the resultant vector is completely represented both in direction and magnitude by the diagonal of the parallelogram passing through the point.

Let R be the resultant of two vectors P and Q.
According to the parallelogram law of vector addition, the resultant R is the diagonal of the parallelogram of which P and Q are the adjacent sides as shown in the figure.

The magnitude of R is given by

where, θ is the angle between P and Q.
Similarly, if we consider P as F₁ and Q as F₂ then the diagonal will be vector F₃.

Concept:

• If a wire is under force, there will be an increase or decrease in length due to the developed stress and strain in it.
  • Normal Stress is calculated by perpendicular Force (F) divided by the cross-section area (A) on which it is applied.

Normal Stress = F/A

• The strain is the change in length of wire (l) divided by the original length (L) of the wire.
  Strain = l/L
• Hook's Law of elasticity Young's modulus = stress/strain

Explanation:
​Given diagram as said in the question:

For the given diagram:
Stress = F/A
Strain = l/L
We know from Hook's law that




So the force required to increase the length of the wire by 'l' is:

Hence the correct answer is option 1.

Concept:

• Equilibrium: It is a state of a body in which overall change in a body is zero.
• Translational Equilibrium: A body is said to be in translational equilibrium if the net sum of all the forces (F) acting on a body is zero.

ΣF = 0
F_net = 0
F₁ + F₂ + F₃ + ............... + F_n = 0

• Rotational Equilibrium: A body is said to be in rotational equilibrium if the net sum of all the torque (τ) acting on a body is zero.

Σ τ = 0
τ_net = 0
τ₁ + τ₂ + τ₃ + .................. + τ_n = 0
Calculation:

• First, draw the FBD of the given figure and resolve it into a horizontal and vertical component
  ​
• Horizontal component

T₁ Cos 30° = 100 Cos 60°
T₁ = 100 / √3 N

• Vertical Component

T₁ Sin 30° + 100 Sin 60° = W
By putting the value of T₁ from above we get
= W
W = 200 / √3 N
Hence option 3 is correct.
Other Related Points

• Solving the numerical problem on the equilibrium of forces always draws the FBD (Fee Body Diagram).
• A simplified version of the body on which all external forces are shown is called FBD (Fee Body Diagram) of the given body.

Reversible Processes:

• A thermodynamic process driving from initial state to final state is said to be reversible, if the system as well as its surrounding returns back to its initial state, without any change in the universe.
• The processes which can be idealized as reversible are Motion without friction, Expansion/ compression with infinitesimal pressure difference, Energy transfer as heat with infinitesimal temperature difference, isothermal and adiabatic.

Irreversible Processes:

• A thermodynamic process that does not return back to its initial state is termed as an irreversible process.
• The examples of irreversible processes are Motion with friction, Throttling, Free expansion, Constant Volume and constant pressure, Expansion/ compression with finite pressure difference, Energy transfer as heat with finite, mixing of matter at different states, Mixing of non-identical gases.

Concept:

• Angular Momentum (L): It is a property of a body in rotational motion.
  • The moment of linear momentum is known as angular momentum.

L = r × p = r × mv
where p is the momentum of the body, r is the distance of linear momentum from the axis of rotation, m is the mass of the body, and v is the velocity of the body.

• Linear momentum Conservation: When in a system, there is no external force then the total momentum (P) of the system will be conserved.
• Angular momentum Conservation: When in a system, there is no external torque then the total angular momentum (L) of the system will be conserved.

Explanation:

• If net external torque on a rotating object is zero, Its angular momentum will be conserved i.e. will be constant.
• Linear momentum is conserved when there is no external force on the body.
• Linear velocity is constant when a body is moving with a constant speed and constant direction.
• The angular velocity of a body is constant if it is moving in a uniform circular motion.
• So the correct answer is option 4.

Law of Parallelogram of forces:
This law is used to determine the resultant of two coplanar forces acting at a point.
It states that “If two forces acting at a point are represented in magnitude and direction by two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram which passes through that common point.”

Let two forces F₁ and F₂, acting at the point O be represented, in magnitude and direction, by the directed line OA and OB inclined at an angle θ with each other.
Then if the parallelogram OACB be completed, the resultant force R will be represented by the diagonal OC.

Calculation:
F₁ = 3 kN, F₂ = 4 kN, θ = 60°
F_R = (3² + 4² + 2 × 3 × 4 cos 60)^1/2
F_R = 6.08 kN

Concept:
Pascal’s Law: it is the principle of transmission of fluid-pressure. It says that "a pressure exerted anywhere in a point of the confined fluid is transmitted equally in all directions throughout the fluid”.
i.e., the pressure exerted by the fluid on an object at a certain height will be the same in all direction and hence it can be expressed as

• The force against area within a fluid at rest will always experience pressure perpendicular to their surface area, and the object will experience equal pressure throughout the surface.
• There are a number of devices, such as hydraulic lift and hydraulic brakes, are based on Pascal’s law.
• These devices used fluids for transmitting pressure.

Hydraulic lift: In a hydraulic lift, as shown in the figure below, two pistons are separated by the space filled with a liquid

Now as Pascal suggested both that the platform will have some pressure although the platform has a different surface area hence the force exerted on surface 2 will be much greater than on force one

Other Related Points
Archimedes principle: It is used to explain law of flotation or upward thrust experienced when immersed in a fluid

• the principle of Archimedes states “When a body is immersed in a liquid, an upward thrust, equal to the weight of the liquid displaced, acts on it.”

i.e., weight of an object = Upward thrust
Here,
F₁, F₂ = force exerted on area A₁ and A₂ respectively
P₁, P₂ = Pressure exerted on area A₁ and A₂ respectively

CONCEPT:

Velocity:

• The rate of change of displacement of an object (displacement over elapsed time) is velocity.
• Velocity is given by,

Acceleration:

• The rate of change of velocity is acceleration.
• Like velocity, acceleration is a vector and has both magnitude and direction.
• Acceleration is given by,

​

CALCULATION:

Given:

The position of a particle as a function of time t (i.e., displacement) is x = t³- 2t² + 2

• Now the velocity will be,

Now at t = 4sec,

The velocity will be,

⇒ v = 3 × 4² - 4 × 4 = 48 - 16 = 32 m/s

⇒ v = 32 m/s

CONCEPT:

• For the maximum intensity we write;

Here I_max is the maximum intensity, and I₁ and I₂ are the intensity in 1 source and 2nd source.

• For the minimum intensity we write;

Here Imin is the minimum intensity, and I1 and I2 are the intensity in 1 source and 2nd source.

CALCULATION:

Given: The two coherent light sources having the intensity in the ratio of 2x which is written as;

⇒

Let, , and

The maximum intensity, I_max =

=

=

The minimum intensity, Imin =

=

=

To calculate: ----(1)

Now, on putting the values in equation (1) we have;

⇒ =

⇒ =

⇒ =

Hence, option 2) is the correct answer.

Concept:

• A simple pendulum consists of a heavy particle suspended from a fixed support through a light inextensible string.
• The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by “T”
• -- (1)

Calculation:
Given data, mass of the bob is doubled, m₁ = 2m and the length of the string is halved, l₁ =
From equation 1 T ∝ √ l and don't depend upon mass of bob.
Then,
⇒

Other Related Points

• The oscillatory motion of a simple pendulum: Oscillatory motion is defined as the to and fro motion of the pendulum in a periodic fashion and the centre point of oscillation known as equilibrium position
• The amplitude of simple pendulum: It is defined as the distance travelled by the pendulum from the equilibrium position to one side.

Concept:

• Average velocity is calculated by dividing your displacement (a vector pointing from your initial position to your final position) by the total time.
• Average speed is calculated by dividing the total distance you traveled by the total time.
  • 

Calculation:

Given: x(t) = αt + βt3 ;where α = 2.0 m/s, β = 0.01 m/s3

x_f = x_(t=4) = 2 × 4 + 0.01 × 4³

x_(t=4) = 8.64

Similarly,

x_i = x_(t=2) = 2 × 2 + 0.01 × 23

x_(t=2) = 4.08

Therefore,

This is the required velocity.

Concept:
Electrostatic External Field Torque- It is defined as the product of the moment and field and it is written as;
Electrostatic External Field Energy - It is defined as the dot product of moment and the field is written as;
Calculation:
As we know;
Electrostatic External Field Torque- It is defined as the product of the moment and field and it is written as;
​​
Electrostatic External Field Energy - It is defined as the dot product of moment and the field is written as;

The electrostatic axial field for a short dipole - The Electrostatic axial field for a short dipole is written as;

Electrostatic Equatorial Field for a short Dipole is written as;

Hence option (1) is the correct answer.

CONCEPT:

The potential of the given conduction sphere is written as;

V =

⇒ V = k

Here V is the potential, Q is the charge, and k is the constant of proportionality.

CALCULATION:

According to the potential of the condition sphere we have;

V = k

Where R is inversely proportional to the applied potential.

In this question, we have two hollow conducting spheres where R₁ >> R₂. The larger the radius the smaller the potential for the given conducting spheres.

So, R₂ is having large potential than R₁.

Hence, option 3) is the correct answer.