Advertisements
Advertisements
प्रश्न
Solve the numerical example.
When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72'' of arc. Calculate the diameter of Jupiter.
Advertisements
उत्तर
Given: Angular diameter (α) = 35.72''
= 35.72'' × 4.847 × 10-6 rad
≈ 1.73 × 10-4 rad
Distance from Earth (D) = 824.7 million km
= 824.7 × 106 km
= 824.7 × 109 m.
To find: Diameter of Jupiter (d)
Formula: d = α D
Calculation: From the formula,
d = 1.73 × 10-4 × 824.7 × 109
= 1.428 × 108 m
= 1.428 × 105 km
The diameter of Jupiter is 1.428 × 105 km.
APPEARS IN
संबंधित प्रश्न
The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?
500 gm = ______ kilogram.
Ten millimetre makes one centimetre.
Match the following.
| 1. | Length of the fore arm | metre |
| 2. | SI unit of length | second |
| 3. | Nano | 103 |
| 4. | SI Unit of time | 10–9 |
| 5. | Kilo | Cubit |
Fill in the following chart.
| Property | Definition | Basic Unit | Instrument used for measuring |
| Length | |||
| Mass | |||
| Volume | |||
| Time |
Rulers, measuring tapes and metre scales are used to measure ______
Metre is the unit of ______.
Can you find the diameter of a thin wire of length 2 m using the ruler from your instrument box?
Have you seen frogs? Where? How many different types of frogs have you seen? Are all the frogs of the same length? Here are two interesting examples.
Guess the lengths to draw these things. Ask your friend to draw the same. After you make the drawing use a scale to measure the length. Whose drawing showed a better guess?
| Guess its length and draw |
Measure of your drawing |
Measure of your friend’s drawing |
| An ant of length less than 1 cm |
||
| Pencil of length about 7 cm |
||
| A glass 11 cm high with water up to 5 cm |
||
| A bangle of perimeter 20 cm |
||
| A curly hair of length 16 cm |
What is the length of a 100 rupee note? Guess. Now measure it using a scale.
Now guess the length and width of many other things. Measure and find the difference between your measure and your guess.
| Size of | Your guess in cm | Your measure in cm | ||
| Length | Width | Length | Width | |
| 100 Rupee note | ||||
| 10 Rupee note | ||||
| 20 Rupee note | ||||
| 5 Rupee note | ||||
| Post card | ||||
| Math-Magic book | ||||
Measure the yellow rectangle. It is ________ cm long.
How many stamps are needed to cover the rectangle?
The fencing of a square garden is 20 m in length. How long is one side of the garden?
Chumki, Jhumri, and Imran need wire to make a fence.
- How much wire in all will the three need?
There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.
- How many cm is the length of the boundary of lake A in the drawing?(use thread to find out)
There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.
- Find the area of lake B on the drawing in square cm. What is its actual area in square km?
In which SI unit, you can measure your height?
Length is a fundamental quantity.
Match the following:
| Prefix | Symbol | ||
| a. | Centi | i. | k |
| b. | Nano | ii. | c |
| c. | Mili | iii. | n |
| d. | Kilo | iv. | m |
What is the unit of measurements of very small lengths?
What is the unit of length?
To measure the distance of a planet from the earth, ______ method is used.
The radius of atom is of the order of 1 Å and the radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?
In an experiment to estimate the size of a molecule of oleic acid 1 mL of oleic acid is dissolved in 19 mL of alcohol. Then 1 mL of this solution is diluted to 20 mL by adding alcohol. Now 1 drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water forming one molecule thick layer. Now, lycopodium powder is sprinkled evenly over the film and its diameter is measured. Knowing the volume of the drop and area of the film we can calculate the thickness of the film which will give us the size of oleic acid molecule.
Read the passage carefully and answer the following questions:
- Why do we dissolve oleic acid in alcohol?
- What is the role of lycopodium powder?
- What would be the volume of oleic acid in each mL of solution prepared?
- How will you calculate the volume of n drops of this solution of oleic acid?
- What will be the volume of oleic acid in one drop of this solution?
How many astronomical units (A.U.) make 1 parsec?
If a planet subtends an angle α at distance D, what formula is used to find the planet's diameter?
