Problem 820 - JEE Physics

Question

Direction (Read the following questions and choose) (A) If both Assertion and Reason are true and the Reason is correct explanation of assertion (B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion (C) If Assertion is true, but the Reason is false (D) If Assertion is false, but the Reason is true Assertion: The time period of a geostationary satellite is 24 hours Reason: Such a satellite must have the same time period as the time taken by the earth to complete one revolution about its axis (a) \(\mathrm{A}\) (b) B (c) \(\mathrm{C}\) (d) D

Step-by-Step Solution

Answer

The correct answer is (a) A, as both the Assertion and Reason are true, and the Reason provides the correct explanation for the Assertion. A geostationary satellite has a time period of 24 hours because it orbits the Earth at the same rate as the Earth rotates, causing it to appear stationary when observed from the Earth's surface.

Step 1: Determine if the Assertion is true

A geostationary satellite is a satellite that orbits the Earth at the same rate as the Earth rotates, such that it appears to be stationary when observed from the Earth's surface. Hence, its time period would be equal to the time taken by Earth to complete one revolution about its axis, which we know to be 24 hours. Therefore, the Assertion is true.

Step 2: Determine if the Reason is true

The statement in the Reason says that a geostationary satellite must have the same time period as the time taken by Earth to complete one revolution about its axis. As we mentioned earlier, this is the property of a geostationary satellite, so the Reason is also true.

Step 3: Determine if the Reason is the correct explanation of the Assertion

Since a geostationary satellite orbits the Earth at the same rate as the Earth rotates, the satellite's time period would be equal to the Earth's time period of rotation, which is 24 hours. Thus, the Reason accurately explains the Assertion.

Step 4: Choose the correct option

According to our analysis, both the Assertion and Reason are true, and the Reason is the correct explanation of the Assertion. Therefore, option (a) A is the correct answer.

Key Concepts

Time Period

The term "time period" refers to the time it takes for a repeating event to occur once. In the context of a geostationary satellite, its time period is crucial.
For these satellites, the time period is exactly 24 hours.
This synchronization with Earth's rotational period allows them to appear motionless in the sky above a fixed point on Earth's surface.
Such synchronization ensures reliable communication and monitoring systems as the satellite maintains a constant view of the same region.

Earth's Rotation

Earth completes one full rotation on its axis approximately every 24 hours. This rotation is what defines one day, transitioning from day to night and back again.
A geostationary satellite orbits at a rate that matches this rotation.
This means that from the surface of the Earth, the satellite appears to hover over the same spot.

• This fixed presence is particularly useful for applications like weather monitoring, telecommunications, and broadcasting.
• Being in sync with Earth's rotation, the satellite can continuously cover the same geographical area.

Satellite Orbit

A geostationary satellite orbits the Earth along the equatorial plane at a specific altitude, approximately 35,786 kilometers above the Earth's surface.
This high orbit allows it to keep pace with the Earth's rotation, maintaining a constant position relative to the Earth's surface.

• The orbit is circular, which is essential for maintaining its position over a fixed point.
• This type of orbit is only possible directly above the equator, making it a unique and valuable orbital path for satellites.

Such positioning advantages make geostationary satellites ideal for long-duration tasks upholding steady communication linkages over particular Earth regions.