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Given:

Speed from A to B = 20 km/hr

Speed from B to A = 30 km/hr

Formula used:

Average speed = Total distance/Total time

Calculation:

Let the distance between A to B be x km

So according to question,

Average speed = 2x/(x/20 + x/30) 

⇒ Average speed = 2x/(5x/60)

∴ Average speed = 24 km/hr

Given:

Speed of A = 45 km/hr

Speed of B = 60 km/hr

A starts at 9 ∶ 00 AM and B starts at 10 ∶ 00 AM

They meet at half distance while travelling in the opposite direction

Concept used:

Distance = Speed × Time

Calculation:

Let the time taken by B to reach half the distance be x hours

Time taken by A to reach half the distance will be x hours + 1 hour = (x + 1) hours

As, they have traveled half distance, i.e they have traveled equal distance

Half distance travelled by A = 45 × (x + 1)

Half distance traveled by B = 60 × x

45x + 45 = 60x

⇒ 15x = 45

⇒ x = 3

Distance travelled by A = 45 × (3 + 1) = 45 × 4 = 180

∴ Distance traveled by A is 180 km

Given:

Speed of A = 36 km/hr = 36 × 5/18 = 10 m/sec

Speed of B = 54 km/hr = 54 × 5/18 = 15 m/sec

Speed of C = 18 km/hr = 18 × 5/18 = 5 m/sec

Formula used: 

Speed = Distance/Time

Calculation:

Time taken by A to complete 1 round = 1200/10 = 120 seconds

Time taken by B to complete 1 round = 1200/15 = 80 seconds

Time taken by C to complete 1 round = 1200/5 = 240 seconds

∴ The meeting time will be LCM of (120, 80, 240) i.e = 240 seconds

Given:

A rabbit runs 6 km at a speed of 3km/h

Average speed of the entire distance covered = 6 km/h

Formula Used:

Average Speed = Total Distance/ Total Time

Calculation:

Let the speed of the rabbit be S km/h for next 3 hours

Distance covered in 3 hours = 3 × S km

⇒ 3S km

Time taken to cover 6 km at a speed of 3km/h = 6/3

⇒ 2 hours

Average speed = (6 + 3S)/(2 + 3)

⇒ (6 + 3S)/5 = 6 

⇒ 3S = 30 – 6 km/h

⇒ S = 24/3 km/h

⇒ S = 8 km/h

∴ The speed of the rabbit is 8 km/h for next 3 hours so that average speed is 6 km/h through out the journey.

Correct option is C) winter

The local time is different at different longitudes. If the same country follows different time, this may create a lot of confusions and problems. So the longitude passing almost through the middle of the country is considered as the standard meridian. The local time at this longitude is considered as the standard Time.

Arunachal Pradesh.

Correct answer is (iv) 6 months of night

60° E 2 pm Monday. \(\frac{60}{15}\) = 4 hours. 10am + 4 = 2pm.

60° W 6 am Monday . \(\frac{60}{15}\) = 4 hours. 10am -4 = 6 am.

82 \(\frac{1}2\)°E longitude is considered as the standard meridian of India. The line passes almost through the middle of India. Each country in the world considers the longitude that passes almost through its middle as the standard meridian. The longitudinal extent of India is from 68°E to 97°E. This amounts roughly to 30°.

The 82 \(\frac{1}2\)°E longitude passes almost through the middle of these longitudes. So 82\(\frac{1}2\)°E longitude is considered as the standard meridian of India.

The earth experiences the recurrence of winter, summer and the rainy season one after the other. 

Such a change on the earth is known as seasonal change.

longitudinal extent of each time zone 15°.

5 hours 30 minutes

Correct answer is (iii) Sunday 1.30 pm 

Correct answer is d. At 105° E of Greenwich

8.30 am on Monday (2 pm – 5 hrs. 30 min = 8.30 am)

• 82\(\frac{1}2\)°E longitude is the standard meridian of India. The local time of this longitude is generally considered as the common time of India. This is known as Indian Standard Time. 
• The IST is 5\(\frac{1}2\) hours ahead of Greenwich time.

a. Revolution 

b. 365 days and 6 hours 

c. Change in the apparent position of the sun due to the inclination and parallelism of the earth’s axis.

The earth revolves around the sun in an elliptical orbit. This motion which takes one year is known as revolution.

The time difference between India and Greenwich is 514 hours. The Greenwich time will be 7.30 a.m on Sunday. (1p.m – 5 \(\frac{1}2\) hiours = 7.30 am)

March 21 and September 23 are equinoxes. On these days, the sun is vertically over the equator. Both the hemispheres receive equal amount of sunlight. Hence the length of day and night will be equal on these days in both the hemispheres.

Variations in the amount of sunshine received are the basis for the occurrence of different seasons. The apparent position of the sun during the earth’s revolution will be over the equator on March 21 and September 23. Hence the length of day and night will be equal during these days on both the hemispheres. These days are called Equinoxes.

The apparent position of the sun shifts from the equator to the northern hemisphere from March 21 to June 21. The sun will be vertically above the tropic of cancer on June 21. This day is known as Summer solstice. lt has the longest day in northern hemisphere and the longest night in southern hemisphere. From June 21 onward, the sun shifts from the tropic of cancer towards the equator and reaches vertically over the equator on September 23.As the sun is in the northern hemisphere from March to September, it will be summer in the northern hemisphere.

The sun continues its apparent movement from the equator to the southern atmosphere and reaches vertically above the Tropic of Capricorn on December 22. This day is known as Winter solstice. During the period from September to March, it will be winter in the northern atmosphere and summer in the southern atmosphere.

The earth takes 365 days, 5 hours, 48 minutes and 45 seconds to complete one revolution (365 \(\frac{1}4\) days).

• Rotation and occurrence of day and night. 
• Tilt of the earth’s axis and revolution.

Variations in the amount of sunshine received are the basis for the occurrence of different seasons. The earth’s revolution and the tilt of the axis are the reasons for this variation.

• Revolution of the earth 
• Tilt of the earth’s axis 
• Parallelism of the earth’s axis 
• The apparent movement of the sun.

The word equinox is derived from the Greek words equi and noxe. ‘Equi’ means equal and ‘noxe’ means night. The word solstices derived from the Greek words sol and stic. Sol means sun and stic means stationary state.

Due to the apparent movement of the sun.

The apparent movement of the sun due to the inclination of axis is the main reason for the occurrence of seasons.

Equal amount of sunlight.

Since the earth maintains its parallelism throughout the revolution, the position of the sun is in relation to the earth varies. The sum shifts apparently between Tropic of Cancer (23 1/2 °North) and Tropic of Capricorn (23 1/2 °South). This is known as the apparent movement of the sun.

The axis of the earth is tilled at an angle of 66 1/2 from the orbital plane. If measured from the vertical plane this would be 23 1/2°The earth maintains this tilt throughout its revolution. This is known as the parallelism of the earth’s axis.

Correct option: b. B only

• The travellers who cross this line from the west calculate time by advancing the day and those who cross the line from the east deduct one day. 
• The travellers who cross the International Date Line from east to west gain a day and those who cross from west to east, lose a day.

On 21^st March, the sun rays are overhead the equator, 0°. So the days and nights are of equal duration, namely 12 hours at all places on the earth. This is called equinoxes. On June 21st, sun appears overhead at the tropic of cancer. This is called summer solstice, and it makes the summer season in the Northern Hemisphere.

On September 23^rd , the sun is overhead at the equator and experiences equinoxes that means equal days and nights. On 22^nd December, the sun continues its apparent movement from the equator to the Southern Hemisphere and reaches vertically above the tropic of capricon. This is called winter solstice.

a. Tropic of Capricorn 

b. Tropic of cancer 

c. Shortest night 

d. Longest night 

e. Longest night 

f. Shortest night

g. Winter solstice 

h. Summer solstice

• b is the wrong answer
• The duration of night in the northern hemisphere decreases from 21 March to 21 June.

The 180° longitude line from the east and west of Greenwich line is the International Date Line. There is a time difference of 24 hours on both the sides of this line. It creates much difficulty if the same place records two different times with 24 hours difference. To solve this problem, adjustments have been made avoiding the land area along the 180° longitude.

The line is in such a way that it passes through Bering Strait in the Pacific Ocean and avoids some of the inhabited islands. So the International Date Line is not a straight line. The travellers who cross this line from the west calculate time by advancing one day and those who cross the line from the east deduct one day.

21 March – The sun comes vertically over head at the Equator – The duration of day and night are equal on both the hemispheres- Equinox

21 June – The sun is vertically overhead at the Tropic of cancer – The longest day in the northern hemisphere and longest night in the southern hemisphere – Summer solstice

23 September – The sun comes vertically overhead at the equator – The duration of day and night are equal on both the hemispheres- Equinox

22 December -The sun is vertically over head at the tropic of Capricorn – The longest day in the southern hemisphere and longest night in the northern hemisphere – Winter solstice

• Day and night are caused due to rotation. 
• It takes 24 hours to complete one rotation. 
• The earth rotates from west to east and so the sun rises in the eastern side.

• The time estimated at each place based on the apex position of the sun is known as local time. 
• The local time is not the same at each place in India. 
• If there are several local times in a country, it leads to complications like:

a. Cannot prepare a railway, plane and ship time. table applicable throughout the country. 

b. Cannot give information on radio and television programs. 

c. Inconvenience in the time schedule of National Day celebrations.

Summer season is experienced in Northern Hemisphere during June 21 and September 23. 

Peculiarities of Summer

• Vertical sun rays and more sunlight. 
• Warm atmosphere.

The sun would be always near the equator if the earth’s axis was not tilted. Sun rays fall vertically near the equator and the atmosphere gets heated excessively. Consequences:

• Both the hemispheres receive equal amount of sunlight. 
• Equatorial regions experience high temperatures always. 
• No change in seasons 
• Duration of day and night will be equal.

a. 0° latitude or equator experiences equal day and night. 

b. 6 months. This is because the sun is in the Northern Hemisphere. 

c. 90°N.