email: [email protected] What is October heat

3
email: [email protected] þ¼÷ªî¦ô¢Ù 16 è…šúÙñô¢ª 2019 1 Mark Questions 1. What is disguised unemployment? A: The workers who are working less than their full capacity is called disguised unem- ployment. 2. What is meant by final goods and services? A: Final goods and services refer to the goods and services which are meant either for consumption by consumers or for invest- ment by firms. 3. Who are called marginal farmers? A: A farmer who can grow crops for his family members sake only. 4. What are intermediate goods? A: Intermediate goods are those goods which are used in producing final goods and services. 5. Mention any two aspects of primary sector? A: Agriculture, Mining 6. Give any two examples come under sec- ondary sector? A: Manufacturing operations in industries both large and small and also included in con- traction activity. 2 Marks Questions 1. ‘The workers in agricultural sector are under developed’ Explain. A: There are more people in agriculture than is necessary. Each one is doing some work but no one is fully employed. This is the sit- uation of disguised unemployment, where people are apparently working but all of them are made to work less than their potential. 2. How is the organised sector different from an unorganised sector? A: H The organised sector in the enterprises or places of work where the terms of employment are regular and therefore people have assured work. H The unorganised sector is characterised by small and scattered units which have remained largely outside the control of the government. In this way organised sector is different from unorganised sector. 3. Briefly mention the differences between intermediate goods and final goods with examples. 4. Explain various programmes launched by government for promotion of employment? A: The various programmes launched by Government for promotion of employment are 1) Rural Works Programme 2) National Rural Employment Programme (NREP) 3) Marginal Farmers and Agricultural Labourers (MFAL) scheme 4) Small Farmers Development Agencies Kanukolanu Srinivas Rao Subject Expert Writer Target-2020 Tenth Social Studies Paper- I 100 100 Production and Employment A: Intermediate goods 1) These goods are meant for further production 2) These are not included in GDP Final goods 1) These are used for final consump- tion 2) These are includ- ed in GDP 1. ‘The importance of the service sector is going on increasing day by day’ Do you support this statement why? (AS2) A: 1) Yes, I support the statement that the importance of the service sector is going on increasing day by day. 2) Though service sector does not produce goods, it strengthens the needs of the other two sectors. 3) The basic services like community, social, personal services, finance, insurance and real estate, trade hotels, transport and communication are very essential and pro- vides wide range of employment opportuni- ties and large share of GDP. 2. Read the table and fill in the blanks. (AS3) 1) Majority of workers in agriculture are living in...... A: Rural areas 2) Most......workers are employed in agricul- ture sector. Only a small section of....is in Industrial sector. A: Female, Female 3) More than 90% of urban workers are get- ting employment in......and ......sectors. A: Industrial, Service 4) Compared to males, female workers are getting employment in...... and ...... sec- tors only to a small extent. A: Agriculture, Industrial 4 Marks Questions Distribution of workers in India 2009-10(%) Place of Residence Sex All workers Sector Rural Urban Male Female Agriculture 68 8 47 69 53 Industry 17 34 34 16 22 Service 15 58 19 15 25 Total 100 100 100 100 100 The Climate of India 2 Marks Questions 1. How does deforestation affect global warm- ing? A: 1) Number of trees are decreasing due to deforestation. 2) During photosynthesis plants convert car- bon dioxide (CO 2 ), Carbon Monoxide (CO) into oxygen. 3) Due to felling of trees, the amount of CO 2 and CO increase in the atmosphere. 4) These gases are responsible for green house effect or global warming. 2. Write any four human actions contribute to global warming. A: 1) Use of fertilizers and pesticides 2) Fossil fuel combustion and rice fields 3) Coal mines and natural gas leaks 4) Refrigerators 3. What is known as weather and climate? A: 1) The state of atmospheric conditions over an area at a particular time refers to weather. 2) Average conditions over a large area and follows a similar general pattern over many years (30 years or more) refer as the climate. 4. Why does Darjeeling have pleasant weath- er as compared to Kolkata during summer season? A: 1) 1°C of temperature will decreases at every 165 metre altitude increase. 2) Hence Darjeeling which is situated on higher altitude than Kolkata experience pleasant weather during summer sea- son. 5. Why is Indian agriculture a gambling with monsoon? A: 1) Agriculture in India depends on monsoon rains. The rains are uncertain, irregular and uneven as such they hamper our agriculture development. 3) Droughts and floods are quite common here. These calamities have an adverse effect on the economic development of India. Hence Indian agriculture is referred to as a gamble in the monsoons. 6. Read the following lines and answer the fol- lowing question. (AS2) The retreat of the monsoons is marked by clear skies and rise in temperature. The land is still moist. Owing to the conditions of high tem- perature and humidity. The weather becomes rather oppressive. This is commonly known as ‘October heat’. 7. Write main characteristics of retreating mon- soon. A: During this season the monsoon becomes weak and is replaced by high pressure. Thus the monsoon begins to retreat. This period of transition from hot rainy season to cold winter season. It is marked by clear sky, moist ground and high temperature giving birth to October heat. 1. What are Climographs? A: Climographs show average monthly values maximum temperature, minimum tempera- ture and rainfall for a given place. 2. What is global warming? A: The atmosphere traps a lot of solar energy by preventing it from totally escaping back into space is called global warming. 3. Mention any two human activities which contribute to global warming? A: 1) Deforestation 2) Industrialisation 4. What is deforestation? A: Deforestation is cutting down and clearing away forest on a very large scale. 5. Write down the two characteristics of the tropical climate? A: 1) High temperatures 2) Heavy precipitation throughout the year 1. Observe the following climographs and answer. (AS3) 1) Which months received the highest and the lowest temperature? A: Highest - May, Lowest - December 2) Which month recorded the highest rain- fall? A: August 3) Why is the maximum amount of rainfall between June and October? A: Due to advancing South-West monsoons. 4) Why is the temperature high between March and May? A: The sun rays shine vertically in this region. Additional Questions 1. Describe India’s climate controls? 2. What are disagreements between devel- oped and developing countries about AGW? 3. How are human activities contributing to Global warming? 4. ‘Now a days Himalayas have a great influ- ence on India’s climate’ Explain. 4 Marks Questions 1 Mark Questions What is October heat ? 1 2 Mark Questions 1. .... is a more powerful as a greenhouse gas. A: Methane 2. AGW - ‘A’ stands for.... A: Anthropogenic (human) 3. Find the incorrect set. Vasantha - March to April, Grishma - May to June, Sharad - September to October, Hemantha - January to February A: Hemantha ( November to December) 4. The gas that protects us from harmful ultraviolet rays is.... A: Ozone 5. During the last few decades many glaci- ers have melted in Himalayas. It is an example of..... A: Global warming 6. One of the human activities that con- tribute global warming is…. A: Deforestation or burning fossil fuels Rain Fall (mm) Temperature ( 0 c) Mean Rain Fall Hyderabad 17.4 o N, 78.5 o N February March April May June July August September October November December 0.0 0 5 10 15 20 25 30 35 40 45 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0 Maximum Temperature Minimum Temperature January

Transcript of email: [email protected] What is October heat

email: [email protected]þ¼÷ªî¦ô¢Ù 16 è…šúÙñô¢ª 2019

1 Mark Questions

1. What is disguised unemployment?A: The workers who are working less than

their full capacity is called disguised unem-ployment.

2. What is meant by final goods and services?A: Final goods and services refer to the goods

and services which are meant either forconsumption by consumers or for invest-ment by firms.

3. Who are called marginal farmers?A: A farmer who can grow crops for his family

members sake only.4. What are intermediate goods?A: Intermediate goods are those goods which

are used in producing final goods and services.

5. Mention any two aspects of primary sector?A: Agriculture, Mining6. Give any two examples come under sec-

ondary sector?A: Manufacturing operations in industries both

large and small and also included in con-traction activity.

2 Marks Questions

1. ‘The workers in agricultural sector are underdeveloped’ Explain.

A: There are more people in agriculture than isnecessary. Each one is doing some workbut no one is fully employed. This is the sit-uation of disguised unemployment, wherepeople are apparently working but all ofthem are made to work less than theirpotential.

2. How is the organised sector different froman unorganised sector?

A: H The organised sector in the enterprisesor places of work where the terms ofemployment are regular and thereforepeople have assured work.

H The unorganised sector is characterised bysmall and scattered units which haveremained largely outside the control of thegovernment.In this way organised sector is different from

unorganised sector.3. Briefly mention the differences between

intermediate goods and final goods withexamples.

4. Explain various programmes launched bygovernment for promotion of employment?

A: The various programmes launched byGovernment for promotion of employmentare1) Rural Works Programme 2) National Rural Employment Programme

(NREP)3) Marginal Farmers and Agricultural

Labourers (MFAL) scheme 4) Small Farmers Development Agencies

Kanukolanu Srinivas RaoSubject Expert

WriterTarget-2020

TenthSocial Studies Paper- I

100100

Production and Employment

A: Intermediategoods

1) These goods aremeant for furtherproduction

2) These are notincluded in GDP

Final goods

1) These are usedfor final consump-tion

2) These are includ-ed in GDP

1. ‘The importance of the service sector isgoing on increasing day by day’ Do yousupport this statement why? (AS2)

A: 1) Yes, I support the statement that theimportance of the service sector isgoing on increasing day by day.

2) Though service sector does not producegoods, it strengthens the needs of theother two sectors.

3) The basic services like community, social,personal services, finance, insurance andreal estate, trade hotels, transport andcommunication are very essential and pro-vides wide range of employment opportuni-ties and large share of GDP.

2. Read the table and fill in the blanks. (AS3)

1) Majority of workers in agriculture are livingin...... A: Rural areas

2) Most......workers are employed in agricul-ture sector. Only a small section of....is inIndustrial sector. A: Female, Female

3) More than 90% of urban workers are get-ting employment in......and ......sectors.

A: Industrial, Service4) Compared to males, female workers are

getting employment in...... and ...... sec-tors only to a small extent.

A: Agriculture, Industrial

4 Marks Questions

Distribution of workers in India 2009-10(%)Place of Residence Sex All workers

Sector Rural Urban Male Female

Agriculture 68 8 47 69 53

Industry 17 34 34 16 22

Service 15 58 19 15 25

Total 100 100 100 100 100

The Climate of India

2 Marks Questions

1. How does deforestation affect global warm-ing?

A: 1) Number of trees are decreasing due todeforestation.

2) During photosynthesis plants convert car-bon dioxide (CO2), Carbon Monoxide (CO)into oxygen.

3) Due to felling of trees, the amount of CO2and CO increase in the atmosphere.

4) These gases are responsible for greenhouse effect or global warming.

2. Write any four human actions contribute toglobal warming.

A: 1) Use of fertilizers and pesticides2) Fossil fuel combustion and rice fields3) Coal mines and natural gas leaks4) Refrigerators

3. What is known as weather and climate?A: 1) The state of atmospheric conditions over

an area at a particular time refers toweather.

2) Average conditions over a large area andfollows a similar general pattern overmany years (30 years or more) refer asthe climate.

4. Why does Darjeeling have pleasant weath-er as compared to Kolkata during summerseason?

A: 1) 1°C of temperature will decreases at

every 165 metre altitude increase.2) Hence Darjeeling which is situated on

higher altitude than Kolkata experiencepleasant weather during summer sea-son.

5. Why is Indian agriculture a gambling withmonsoon?

A: 1) Agriculture in India depends on monsoonrains. The rains are uncertain, irregularand uneven as such they hamper ouragriculture development.

3) Droughts and floods are quite commonhere. These calamities have an adverseeffect on the economic development ofIndia. Hence Indian agriculture is referred to asa gamble in the monsoons.

6. Read the following lines and answer the fol-lowing question. (AS2)

The retreat of the monsoons is marked byclear skies and rise in temperature. The land isstill moist. Owing to the conditions of high tem-perature and humidity. The weather becomesrather oppressive. This is commonly known as‘October heat’.7. Write main characteristics of retreating mon-

soon.A: During this season the monsoon becomes

weak and is replaced by high pressure.Thus the monsoon begins to retreat. Thisperiod of transition from hot rainy season tocold winter season. It is marked by clearsky, moist ground and high temperaturegiving birth to October heat.

1. What are Climographs?A: Climographs show average monthly values

maximum temperature, minimum tempera-ture and rainfall for a given place.

2. What is global warming?A: The atmosphere traps a lot of solar energy

by preventing it from totally escaping backinto space is called global warming.

3. Mention any two human activities whichcontribute to global warming?

A: 1) Deforestation 2) Industrialisation4. What is deforestation?A: Deforestation is cutting down and clearing

away forest on a very large scale.5. Write down the two characteristics of the

tropical climate?A: 1) High temperatures

2) Heavy precipitation throughout the year

1. Observe the following climographs andanswer. (AS3)

1) Which months received the highest andthe lowest temperature?

A: Highest - May, Lowest - December

2) Which month recorded the highest rain-fall?

A: August3) Why is the maximum amount of rainfall

between June and October?A: Due to advancing South-West monsoons.4) Why is the temperature high between

March and May?A: The sun rays shine vertically in this

region.

Additional Questions

1. Describe India’s climate controls?2. What are disagreements between devel-

oped and developing countries aboutAGW?

3. How are human activities contributing toGlobal warming?

4. ‘Now a days Himalayas have a great influ-ence on India’s climate’ Explain.

4 Marks Questions1 Mark Questions

What is October heat?

1⎯2

Mark Questions

1. .... is a more powerful as a greenhousegas. A: Methane

2. AGW - ‘A’ stands for.... A: Anthropogenic (human)

3. Find the incorrect set.Vasantha - March to April, Grishma -May to June, Sharad - September toOctober, Hemantha - January toFebruary A: Hemantha ( November to December)

4. The gas that protects us from harmfulultraviolet rays is.... A: Ozone

5. During the last few decades many glaci-ers have melted in Himalayas. It is anexample of..... A: Global warming

6. One of the human activities that con-tribute global warming is….

A: Deforestation or burning fossil fuels

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Hyderabad 17.4o N, 78.5o N

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Janu

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email: [email protected]þ¼÷ªî¦ô¢Ù 16 è…šúÙñô¢ª 2019

1 Mark Questions

1. What is per capita income?A: The total National income divided by num-

ber of people in the Nation.2. What is National Income?A: The income of all the residents of the country.3. What is Infant Mortality Rate?A: The rate at which children in a country die

with in age of 0 - 1 year is known as InfantMortality Rate.

4. What is a Literacy Rate?A: It measures the percentage of literate pop-

ulation in the 7 and above age group.5. Which organisation publishes HDR?A: UNDP publishes the Human Development

Report (HDR).6. Why are dams opposed?A: Dams are opposed because they will dis-

rupt the lives of the people and submergetheir own lands.

7. Write any one advantage of public facilities?A: It develops National feelings and a sense of

collective responsibility.8. In which state of our country “The school

revolution” introduced?A: In Himachal Pradesh the school revolution

is introduced.

2 Marks Questions1. What is the relationship between womens

work outside their homes and gender bias?A: Working women also expect their daughters

to work outside the home after marriage.There is an inverse relationship betweenworking women and gender bias. We wit-ness lower gender bias against women whowork outside their homes as they enjoyrespect from the family and society.

2. In your view those aspects, should be incor-porated in to the administration to measureHuman Development?

A: Factors taken into administration to mea-sure psychological development

1) Per capita income 2) Position of education 3) Position of health

Others to be taken into administration1) Social justice 2) Distibutary system 3) Drinking water 4) Environment and sanitation 5) Electricity 6) Transportation 7) Symbolic progress 8) Life proof3. What are the issues of conflict between gov-

ernment and the people living in regions ofnuclear power plant?

A: H The government of india setup thenuclear power plant in this quiet coastaltown of fisher forks

H The aim is to generate nuclear power to meetthe growing energy needs of the country.

H The people in the region have protected onthe grounds of safety, security and livelihood.

H The people near the plant wanted to look torenewable energy as an alternative.

4 Marks Questions

1. Why do you think parents accord less prior-ity to girls education as compared to boys?

A: H Parents give less priority to girls educa-tion compared to boys

H The main reason behind this is gender bias.H Parents believe that boy is their heir and

spreads their clan.H As marriage institution provides for the girls

to live with husbands family, her parentstake less care about her education.

H Well educated girl needed to be married offto still better educated suitor, an expensiveaffair.

H Girls are engaged in taking care of theirsmaller siblings, which obstructs their edu-cational chances.

H In rural areas girls are married off at earlyages, which prevents their education.

2. What is the per capita income of HimachalPradesh? Do you think higher incomes canmake it easier for parents to send children toschool? Discuss why was it necessary forthe government to run schools in HimachalPradesh?

A: H The per capita income of HimachalPradesh in 2012 is Rs. 74,000.

H Higher income can make it easier for par-ents to send their children to school.

H If the incomes are meague, then parentscannot spend money on education of theirchildren.

H Then children ought to supplement with theirlabour to run the family.

H If higher incomes are there for family, thesecan be avoided.

H Himachal Pradesh had very low levels ofeducation at the time of independence.

H Being a hilly region with low density of pop-ulation in many villages, spread of schoolsis a big challenge.

H So, It was necessary for government to runschools in Himachal Pradesh.

G. Viswa PrasadSubject Expert

WriterTarget-2020

TenthSocial Studies Paper- I

100100

Ideas of Development

1. Expand UNDP (1 M)2. What is HDI (1 M)3. Which countries are called high income

countries? (1 M)4. Explain about the Human Development

Report? (2 M)5. Why do we need public facilities? who

provide public facilities? (4 M)

Additional Questions

4 Marks Questions

1. How is the service sector different fromother sectors?

A: H Service sector is different from the othertwo sectors, Agriculture and Industry.

H Agriculture and Industry sectors producegoods whereas service sector does notproduce any good.

H In agriculture and in Industrial sector theyneed the help of service sector in the pro-duction of their goods.

H But service sector does not need the helpof agriculture or industry in its service.

H Without service sector the needs of peoplefor their physical and mental growth are notfulfilled.

H Service sector is the lifeline of people.H Growth in service sector indicates modern-

ization.2. Why it’s important to protect and support the

workers in the unorganized sector? Explain.A: It is important to protect and support the

workers in the unorganized sector asworkers are exploited in this sector. It isbecause in unorganized sectors, the gov-ernments rules and regulations regardingthe conditions of employment are not fol-lowed often jobs are low paid and irregu-lar. Workers have to work for longer hours

with no provision of overtime they are nei-ther given paid leaves or any medical ben-efits. There is no job security and theemployer can ask an employee to leave, incase of lean season.

3. What are the changes in shares of differentsectors in GDP?

A: H There have been many developmentsthat changed today’s economic priorities.

H A major role has been played by scienceand technology.

H The emergence of industries promoted thesecondary and tertiary sector and providedjob opportunities to many people.

H This made many people to migrate fromprimary to secondary and tertiary sectors.

1. Suggest any two measures to create moreemployment in rural India?

A: H Irrigation facilities should be improvedfor agriculture land.

H Roads should be constructed.H More education and health facilities should

be provided.H Agro - based Industries should be encour-

aged.2. Describe any four problems faced by work-

ers in unorganized sector?A: H This sector follows no government rules

and regulations.H There is no regular employmentH They have no Job security.H They have no PF Facilities

3. Why the workers in agricultural sector arein underdevelopment?

A: H There are more people in agriculturethan is necessary.

H So even if few people move out productionwill not be affected.

H In other words workers in agricultural sec-tor are underdevelopment.

4. Explain GDP why are only final goods andservices counted in GDP?

A: H GDP - Gross Domestic Product.H GDP is the sum of the money value of final

goods and services produced in each sec-tor during a particular year with in a country.

H Only the value of final goods and servicesare counted in GDP because the value offinal goods already includes the value of allthe intermediate goods.

5. Observe the following Pie charts. AndAnswer the following questions.

i) Which sector is the largest source ofemployment in 1972 - 73

A: Agriculture.ii) What is the table about?A: Sectoral Shares of employment.

Production and Employment

Sectoral Shares of Employment

Services 15%

Industry11% Agriculture

74%

1972

- 73

Services27%

Industry24%

Agriculture49%

2011-12

2 Marks Questions

One Mark Questions

1. In what ways can employment beincreased in urban areas? Write any twosuggestions?

A: H Promotion of Small Scale Industries.H Self-help groups will create.

2. What is meant by ‘final goods and ser-vices’?

A: A final good is a product that the finalconsumer uses or consumes. The gooddoes not require any additional pro-cessing.

3. What is a primary sector?A: Primary sector is the sector which

involves agricultural activities and relat-ed activities like mining, poultry etc.

4. What is disguised unemployment?A: Unemployment which exists when mar-

ginal physical productivity of labour iszero or sometimes it becomes negativeis called disguised unemployment.

5. What are intermediate goods?A: Intermediate goods are those goods

which are used in producing final goodsand services.

6. What is underemployment?A: The state of each one is doing same

work and no one is fully employed.7. Write any two activities which are the

primary responsibility of the govern-ment?

A: Providing water, education, healthfacilities are the primary responsibilitiesof the government.

The School Revolution introduced in?

l

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á:- ÷ú£ªh-÷±ìª θ ÚÁéÙêÁ ví£¤¨í£h٠ඛúh, ÍC à¶ô¢ª-ÚÛªû¶ÞœJù£’ Ó꟪h

υ02 sin2θ

Hmax = ⎯⎯⎯⎯2g

sÏÚÛ\è[ υ0 ê•L-î�¶-Þ¥Eo ú£«#-ú£ªhÙCzυ0

2 sin2 45°θ = 45° Íô³ê¶, Hmax = ⎯⎯⎯⎯⎯

2g

1υ0

2 (⎯⎯)2

√⎯2 υ0

2 = ⎯⎯⎯⎯⎯ = ⎯⎯ ....... (1)

2g 4g

υ02 sin2θî¦uí‡h (R) = ⎯⎯⎯⎯

g

υ02sin90°

θ = 45° Íô³ê¶, R = ⎯⎯⎯⎯g

υ02

= ⎯ ....(2)g

1, 2 ú£Oª-ÚÛ-ô¢-é°õ ìªÙ#υ0

2 1 υ02 R

Hmax = ⎯ = ⎯ (⎯) = ⎯4g 4 g 4

R∴ Hmax = ⎯

4

2.- ú£C-øŒõ ú£÷«Ù-êŸô¢ àŸêŸª-ô¢ª(Äá EóŸª-÷«Eo ›íô•\-ìÙè….- íÆ£LêŸ ú£CøŒ í£J-÷«éÙ, CøŒ-õÚÛª ú£Oª-ÚÛ-ô¢éÙô¦ñ-ådÙè….-

á:- ú£-C-øŒõ ú£÷«Ù-êŸô¢ àŸêŸª-ô¢ª(Äá EóŸª÷ªÙ:- ·ôÙè[ªú£C-øŒ-õìª í£J-÷«-éÙö˺, CøŒö˺ ÖÚÛ GÙë]ª÷± ìªÙ#Uú‡ì ú£÷«Ù-êŸô¢ àŸêŸª-ô¢ª(ÄáÙ óμ³ÚÛ\ ·ôÙè[ª Îú£ìoòÅ¡ªâ°-õêÁ ú£«#›úh, Î GÙë]ª÷± ë¯yô¦ î�μü™x ÚÛô¢gÙí£J-÷«éÙ, CøŒö˺ Î ·ôÙè[ª ú£C-øŒõ íÆ£L-ê¦Eo ú£«#-ú£ªhÙC.-

íÆ£-LêŸ ú£CøŒ í£J-÷«éÙ, CøŒ-õÚÛª ú£Oª-ÚÛ-ô¢éÙ:-

í£-åÙö˺ àŸ«í‡ì NëÅ]ÙÞ¥ OP, OQ ¸ôÜõª A→

, B→

Íû¶ ·ôÙè[ª ú£C-øŒ-õìª ú£«#-ú£ªh-û¦oô³ Íìª-ÚÛªÙë¯Ù.î¦æ¨ ÷ªëÅ]u-Þœõ ÚÁéÙ θ Íìª-ÚÛªÙë¯Ù.- R

→Íû¶C A

→,

B→

õ íÆ£LêŸ ú£C-øŒìª ú£«#-ú£ªhÙC.- SN Íû¶C OPÚ¨Uú‡ì õÙñ-¸ôÜ.

í£åÙ ìªÙ#, OS2 = ON2 + SN2

Ú¥F ON = OP + PN = A + B cosθSN = B sinθ (... ΔPSN ìªÙ#)

OS2 = (A + B cosθ)2 + (B sinθ)2

⇒ R2 = A2 + B2 + 2AB cosθ⎯⎯⎯⎯⎯⎯⎯⎯

⇒ R = √ A2 + B2 + 2AB cosθ ...... (1)

SN SNΔOSN ìªÙ#, tanα = ⎯ = ⎯⎯⎯

ON OP + PNB sinθ

= ⎯⎯⎯A + B cosθ

B sinθ⇒ α = tan−1(⎯⎯⎯) .......(2)

A + B cosθ1, 2 ú£Oª-ÚÛ-ô¢-é°õª íÆ£LêŸ ú£CøŒ í£J-÷«éÙ, CøŒ-õìªú£«#-þ§hô³.-

3.- ¤¨Aá ú£÷«Ù-êŸô¢ CøŒÚÛª Ú•ÙêŸ ÚÁéÙ à¶ú£«h Nú‡-Jì÷ú£ªh í£ëÇ]Ù í£ô¦-÷-õóŸªÙ ÍE àŸ«í£Ùè….-

ví£¤¨í£hÙ à¶ú‡ì êŸô¦yêŸ Þ¥Lö˺ ÓT¸ô ÷ú£ªh-÷±ìª -cví£¸¤-í£ÚÛÙe- ÍÙæ°ô¢ª.- ÷ú£ªh-÷±ìª ví£¤¨í£hÙ à¶ú‡ì ÍìÙ-êŸô¢Ùë¯Ešíj í£E ඛú êŸyô¢éÙ, Eåd-E-õª-÷±Þ¥ Ú¨ÙCÚ¨ í£E-ඛú Þœªô¢ª-ê¦y-ÚÛ-ô¢{é ÷õx ÚÛõª-Þœª-꟪ÙC.-a = −gj

Λsö˶ë¯z ax = 0, ay = −g

ê•L î�¶ÞœÙ Vo ÍÙø‹õª:- Vox = Vo cosθo;Voy = Vo sinθo

ví£-¸¤-í£ÚÛÙ ÷«ô¢_Ùö˺ Ú¥õÙ t ÷ë]Ì ví£¸¤-í£ÚÛ þ§–ìÙP(x, y) Íìª-ÚÛªÙë¯Ù.-x = Vox.t = (Vo cosθo).t

x⇒ t = ⎯⎯⎯⎯ .......(1)

Vocosθo

1 1y = Voy.t − ⎯ gt2 = (Vo sinθo).t − ⎯ gt2

2 2

x 1 x2y = (Vo sinθo).(⎯⎯) − ⎯ g(⎯⎯ )Vocosθo 2 Vo

2 cos2θo

(...

(1) ìªÙ#zg

⇒ y = (tanθo)x − (⎯⎯⎯).x22Vo2 cos2θo

gÏ-ÚÛ\è[, a = tanθo; b = ⎯⎯⎯ Íìª-ÚÛªÙç˶

2Vo2 cos2θo

y = ax − bx2 Í÷±-꟪ÙC.- Ð ú£Oª-ÚÛ-ô¢éÙ í£ô¦-÷-õóŸª ú£Oª-ÚÛ-ô¢-é°Eo ú£«#-ú£ªhÙC.- Ú¥ñæ¨d ví£¸¤-í£ÚÛ÷ú£ªh÷± í£ëÇ]Ù í£ô¦-÷-õóŸªÙ.-

4.- íÆ£ªô¢{-éìª êŸT_Ùචí£ë]ÌÄ-꟪-õìª ›íô•\-ìÙè….-á:- ð§-Lùà à¶óŸªè[Ù:- ú£p-J)-ú£ªhìo êŸö°-õìª ð§Lùà à¶ú‡

íÆ£ªô¢{-éìª êŸT_Ù-àŸ-÷àŸªa.- ›úo--Ú¥õª sêŸö°-õìª ìªìªí£± ඛú í£ë¯-ô¦–õªzî¦è[åÙ:- ú£pJ)-ú£ªhìo ·ôÙè[ª êŸö°õ ÷ªëÅ]u íÆ£ªô¢{-éìªêŸT_Ù-àŸ-è¯-EÚ¨ Ñí£-óμ«-TÙචí£ë¯ô¢–Ù Î êŸö°õ ÷ªëÅ]uú£ìoE ð»ô¢-ö° Ôô¢pè… íÆ£ªô¢{-éìª êŸT_-ú£ªhÙC.- ú£ñª(Fô¢ª, Îô³öËÀ, vUV Oæ¨Ú¨ Ñë¯--ô¢é.-

ò°-öËÀ-ò˶-JÙÞ Ñí£-óμ«-TÙ-àŸè[Ù:- šújÚ¨öËÀ, îμ«æ°ôÂî¦ï£°-û¦õ àŸvÚ¥-õÚÛª, óŸªÙvê¦õ ÷ªëÅ]u òÅ°Þ¥-õÚÛªò˶JÙ-Þœª-õìª Í÷ªJa íÆ£ªô¢{-éìª êŸT_Ù-àŸ-÷àŸªa.-ëů-ô¦-î¦--Ú¥-Ú¥ô¢Ù:- N÷«-û¦õª, ·ôjüŒ‰x, îμ«æ°ô î¦ï£°-û¦õ ö°Ùæ¨ î¦æ¨Ú¨ Þ¥L ÷õx ÚÛL¸Þ íÆ£ªô¢{-éìª êŸT_Ù-àŸ-è¯-EÚ¨ î¦æ¨Ú¨ ví£ê¶u-ÚÛ-îμªiì ÎÚ¥-ô¦Eo ÚÛõª-Þœ-â˶-þ§hô¢ª.-

5.- ì«uåû ·ôÙèÁ Þœ÷ªì EóŸª-÷«Eo êμõ-í£Ùè….- ë¯EìªÙ# Þœ÷ªì ú£Oª-ÚÛ-ô¢éÙ F = ma ìª ô¦ñ-ådÙè….-

á:- ÖÚÛ ÷ú£ªh÷± vë]÷u-î�¶-ÞœÙ-ö˺E ÷«ô¢ªp-¸ôåª Î ÷ú£ªh-÷±šíjví£óμ«-TÙ-#ì ò°ï£°u ñö°-EÚ¨ Íìª-ö˺-÷«-ìª-ð§-êŸÙö˺ÑÙè…, Î ñõÙ í£E-ඛú CøŒ-ö˺û¶ ÑÙåªÙC.- Dû¶oì«uåû ·ôÙèÁ Þœ÷ªì EóŸª÷ªÙ ÍÙæ°ô¢ª.-m vë]-÷u-ô¦P Ñìo ÖÚÛ ÷ú£ªh-÷±šíj F Íû¶ ñõÙ ΔtÚ¥õ-÷u-÷-CÅö˺ í£E-à¶-óŸªè[Ù ÷õx ë¯E î�¶ÞœÙ-ö˺E÷«ô¢ªp Δv, vë]÷u-î�¶-ÞœÙ-ö˺E ÷«ô¢ªp ΔP = m.Δv Í-ìª-ÚÛªÙë¯Ù.- ·ôÙèÁ EóŸª÷ªÙ ví£Ú¥ô¢Ù

ΔP ΔPF ∝ ⎯ öË¶ë¯ F = K. ⎯

Δt Δt

Ï-ÚÛ\è[ K Í-ìª-ð§êŸ ú‡–ô¦ÙÚÛÙ.- Δt → 0 Í÷CÅ Bú£ª-Ú•Ùç˶,

dP d(mv) dvF = K.⎯ = K. ⎯⎯ = K.m. ⎯ = Kma

dt dt dt

dv(... a = ⎯)dt

þ¿-õòÅ¡uÙ ÚÁú£Ù K = 1 Þ¥ Bú£ª-ÚÛªÙç˶ F = ma

6.- ú£Cø‹ õò°ÌÄEo Eô¢y-#Ù#, ë¯E ëÅ]ô¦t-õìª ·ôÙè[ªÑë¯--ô¢-é-õêÁ N÷-JÙ-àŸÙè….-

á:- ·ôÙè[ª ú£CøŒ ô¦øŒ‰õ ú£Cø‹ õñÌÄ í£J-÷«é٠ηôÙè[ª ú£C-øŒõ í£J-÷«-é°õ õò°ÌÄEo î¦æ¨ ÷ªëÅ]u-Þœõšújû ÚÁéÙêÁ Þœªé¨Ù-àŸÞ¥ ÷#aì õò°ÌÄ-EÚ¨ ú£÷«ìÙ.-ú£Cø‹ õò°ÌÄû¶o -c÷vá õñÌÄÙe- ÍE ÍÙæ°ô¢ª.- a

→, b

Íû¶ ·ôÙè[ª ú£C-øŒõ ÷ªëÅ]u-Þœõ ÚÁéÙ θ Í-ô³ê¶ a→ × b

→= |a

→| |b

→|.sinθ n

Λ= ab sinθ.n

Λ

Ï-ÚÛ\è[ nΛ Í-û¶C a

→, b

→ ú£-C-øŒ-õêÁ Ôô¢p-è…ì êŸö°-EÚ¨õÙñ-C-øŒö˺ ÑÙè˶ ví£÷«é ú£CøŒ.-|a→ × b

→| = ab sinθ

Ñ-ë¯--ô¢-éõª:-i) þ§–-ì-ú£-CøŒ (r

→), ñõ ú£CøŒ (F

→) õ ú£Cø‹ õò°ÌÄEo

æ°ôÂ\ (τ→) ÍÙ-æ°ô¢ª.-æ°ôÂ\ (τ→) = r

→ × F→

ii) þ§–-ì-ú£-CøŒ (r→), ¸ô&óŸª vë]÷u-î�¶ÞœÙ (p→) õ ú£Cø‹õò°ÌÄEo ÚÁé©óŸª vë]÷u-î�¶ÞœÙ (L

→) ÍÙ-æ°ô¢ª.-

L→

= r→ × p

ú£-Cø‹ õñÌÄ ëÅ]ô¦tõª:- i) ú£-C-ø‹-õñÌÄÙ ú‡–êŸuÙ-êŸô¢ EóŸª-÷«Eo ð§æ¨Ù-àŸë]ª.- ÍÙç˶ a

→ × b→

≠ b→

× a→

. Ú¥F a→ × b

= −(b→

× a→

) Í-÷±-꟪ÙC.-ii) ú£-Cø‹ õñÌÄÙ NòÅ°Þœ û¦uóŸ«Eo ð§æ¨-ú£ªhÙC.-

a→ × (b

→+ c

→) = (a

→ × b→

) + (a→ × c

→)

iii) ú£-÷«Ù-êŸ-ô¢ÙÞ¥ Ñìo ·ôÙè[ª ú£C-øŒõ ú£C-ø‹-õñÌÄÙøŒŠìuÙ.-|a→ × b

→| = ab sin0° = 0

(... θ = 0° Í-ô³ê¶ sin 0 = 0)

iv) ·ôÙè[ª ú£C-øŒõª õÙñÙÞ¥ ÑÙç˶ ÍÙç˶ θ =- 90°Íô³ê¶ |a

→ × b→

| = ab sin90° = ab

v) iΛ, j

Λ, k

Λõª ÷ô¢ª-ú£Þ¥ X,- Y-, Z - Í-¤¥ö˺x í£ô¢-ú£pô¢

õÙñ-C-øŒö˺ Þœõ ví£÷«é ú£C-øŒõª Íô³ê¶,iΛ

× iΛ

= jΛ

× jΛ

= kΛ

× kΛ

= 0

× jΛ

= kΛ, j

Λ× k

Λ= i

Λ, k

Λ× i

Λ= j

ΛÍ-÷±-ê¦ô³.

email: [email protected]þ¼÷ªî¦ô¢Ù 16 è…šúÙñô¢ª 2019

·ÚÓúÃÓúÃ. ô¦áøË™Üô Nù£óŸª Eí£±éªõª

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S

NP0

Q

θθ α

R→B

A→

H 0.-5 Oªåô¢xòÅ¡ªáÙ ÞœõÖÚÛ ú£÷ª-ò°ï£‚vAòÅ¡ªáÙQô¦{õ ÷ë]ÌÑìo÷´è[ªÚÛé°õ vë]÷u-ô¦P ¸ÚÙvë¯Eo ÚÛìª-ÚÁ\Ùè….- ÚÛé°õ vë]÷u-ô¦-øŒ‰õª ÷ô¢ª-ú£Þ¥ 100 vÞ¥.-, 150 vÞ¥.-, 200 vÞ¥.-

á: í£åÙö˺ àŸ«í‡ì NëÅ]ÙÞ¥ X-, Y- Í-¤¥-õìª ÓÙàŸª-ÚÛªÙç˶ ú£÷ª-ò°ï£‚ vAòÅ¡ª-â°Eo Ôô¢p-JචGÙë]ª-÷±õªO, A, B õ Eô¢«-í£-Ú¥õª ÷ô¢ª-ú£Þ¥ (0, 0),(0.-5, 0), (0.-25, 0.-25-√⎯

3) Í÷±-ê¦ô³.- 100vÞ¥.-, 150 vÞ¥.-, 200 vÞ¥.- vë]÷u-ô¦-øŒ‰õª ÷ô¢ª-ú£Þ¥O, A, B õ ÷ë]Ì Ñû¦oô³.- Íìª-ÚÛªÙç˶,

m1x1 + m2x2 + m3x3X = ⎯⎯⎯⎯⎯m1 + m2 + m3

[(100(0) + 150(0.5) + 200(0.25)]= ⎯⎯⎯⎯⎯⎯⎯

[100 + 150 + 200]

125 5= ⎯ = ⎯ Oª.-

450 18

m1y1 + m2y2 + m3y3Y = ⎯⎯⎯⎯⎯m1 + m2 + m3

[100(0) + 150(0) + 200(0.25√⎯3)]

= ⎯⎯⎯⎯⎯⎯⎯[100 + 150 + 200]

50√⎯3 1

= ⎯⎯ = ⎯⎯ Oª.-450 3√⎯

3

5 1∴ vë]-÷u-ô¦P ¸ÚÙvë] Eô¢«-í£-Ú¥õª (⎯, ⎯⎯ -)- 18 3√⎯

3

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GME.mF = ⎯⎯

RE2

Î ÷ú£ªh÷± vޜ Ñí£-J-êŸõÙ ìªÙ# ë]«ô¢ÙÞ¥àŸL›úh, Þœªô¢ª-ê¦y-ÚÛ-ô¢{é ñö°-EÚ¨ ÷uA-¸ô-ÚÛÙÞ¥ í£Eáô¢-Þ¥L.- ÏC ÷ú£ªh-÷±ö˺ ú‡–A-á-øŒ-Ú¨hÞ¥ EõyÑÙåªÙC.-òÅ¡«Nª ÎÚÛ-ô¢{é ÷õx ÚÛL¸Þ ú‡–A-á-øŒÚ¨h

GMEm=- ⎯⎯

RE÷-ú£ªh-÷±ìª Nø‹yÙ-êŸ-ô¦-üŒÙ-ö˺ڨ î�μü™x NëÅ]ÙÞ¥ ví£¤¨í£hÙ

GMEmà¶óŸ«-õÙç˶ ⎯⎯ Ú¨ ú£÷«-ì-îμªiì ÞœA-á-øŒ-Ú¨hE RE

Ïî¦yL.-1 GMEm

∴ ⎯ mVe2 = ⎯⎯⎯

2 RE

⎯⎯⎯2GME 2GME⇒ Ve

2 = ⎯⎯⎯ ⇒ Ve = √ ⎯⎯⎯RE RE

GMEÚ¥F g = ⎯⎯ Ú¥-ñæ¨d RE

2

⎯⎯⎯⎯⎯⎯GME ⎯⎯

Ve = √ 2.(⎯⎯ ) .RE = √ 2gRERE

2

⎯⎯∴ Ve = (Vi)min = √ 2gRE

Y

X(0, 0) (0.25, 0)

B (0.25, 0.25 √⎯3 )

A(0.5, 0)

150 vÞ¥.

200 vÞ¥.

100 vÞ¥.0

÷ªJÚ•Eo ví£øŒoõª

û¦õªÞœª ÷«ô¢ª\õ ví£øŒoõª

0

Y

X

p(x, y)vο

x

yVoy

= V

osin

θ oVox = Vocosθo

θo

á:-ì«uåûÂ