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Chapter 6: Problem 820

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

Short Answer

Expert verified
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 by step solution

01

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.
02

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.
03

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.
04

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.

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Most popular questions from this chapter

If \(\mathrm{V}_{\mathrm{e}}\) and \(\mathrm{V}_{\mathrm{o}}\) are represent the escape velocity and orbital velocity of satellite corresponding to a circular orbit of -adius \(\mathrm{r}\), then A) \(\mathrm{V}_{\mathrm{e}}=\mathrm{V}_{\mathrm{o}}\) (B) \(\sqrt{2} \mathrm{~V}_{\mathrm{o}}=\mathrm{V}_{\mathrm{e}}\) C) \(\mathrm{V}_{\mathrm{e}}=\left(\mathrm{V}_{\mathrm{O}} / \sqrt{2}\right)\) (D) \(\mathrm{V}_{\mathrm{e}}\) and \(\mathrm{V}_{\mathrm{o}}\) are not related

Two satellites \(\mathrm{A}\) and \(\mathrm{B}\) go round a planet \(\mathrm{p}\) in circular orbits having radii \(4 \mathrm{R}\) and \(\mathrm{R}\) respectively if the speed of the satellite \(\mathrm{A}\) is \(3 \mathrm{~V}\), the speed if satellite \(\mathrm{B}\) will be (A) \(12 \mathrm{~V}\) (B) \(6 \mathrm{~V}\) (C) \(4 / 3 \mathrm{~V}\) (D) \(3 / 2 \mathrm{~V}\)

If the density of small planet is that of the same as that of the earth while the radius of the planet is \(0.2\) times that of the earth, the gravitational acceleration on the surface of the planet is (A) \(0.2 \mathrm{~g}\) (B) \(0.4 \mathrm{~g}\) (C) \(2 \mathrm{~g}\) (D) \(4 \mathrm{~g}\)

Escape velocity of a body of \(1 \mathrm{~kg}\) on a planet is $100 \mathrm{~ms}^{-1}$. Gravitational potential energy of the body at the planet is \(=\) $\begin{array}{ll}\text { (A) } \overline{-5000} & \text { (B) }-1000\end{array}$ (C) \(-2400\) (D) 5000

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If the radius of the earth is \(\mathrm{R}\), the radius of planet would be (A) \(2 \mathrm{R}\) (B) \(4 \mathrm{R}\) (C) \(1 / 4 \mathrm{R}\) (D) \(\mathrm{R} / 2\)
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