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Chapter 6: Problem 821

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: Even when orbit of a satellite is elliptical, its plane of rotation passes through the center of earth Reason: This is in accordance with the principle of conservation of angular momentum (a) \(\mathrm{A}\) (b) B (c) \(\mathrm{C}\) (d) \(\mathrm{D}\)

Short Answer

Expert verified
The correct answer is (a) A, as both the assertion and reason are true, and the principle of conservation of angular momentum accurately explains why the plane of rotation of a satellite with an elliptical orbit passes through Earth's center.

Step by step solution

01

Understand Satellite's Orbit

The assertion claims that even if a satellite has an elliptical orbit, the plane of rotation of the satellite passes through the center of the Earth. This means that when a satellite orbits the Earth, its path always lies on a plane (2D surface) that passes through Earth's center. #Step 2: Understanding the Reason#
02

Connect with the Principle of Conservation of Angular Momentum

The reason provided is the principle of conservation of angular momentum, which states that the angular momentum of a system remains constant if no external torques act on the system. It implies that if the satellite is not affected by external factors, its angular momentum will be conserved and should follow a certain trajectory or path in its orbit. #Step 3: Check if the Reason Conforms to the Assertion#
03

Check for the Relation Between Angular Momentum and the Assertion

As the satellite orbits Earth, its path conforms to the conservation of angular momentum. According to this principle, the path of the satellite must be in a plane that passes through the center of the Earth. #Step 4: Determine the Correct Answer#
04

Choose the Appropriate Option

Since both the assertion and reason are correct, and the principle of conservation of angular momentum accurately explains why the plane of rotation of a satellite with an elliptical orbit passes through Earth's center, we can opt for the correct answer: (a) A

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Most popular questions from this chapter

The escape velocity for a sphere of mass \(\mathrm{m}\) from earth having mass \(\mathrm{M}\) and Radius \(\mathrm{R}\) mass is given by (A) \(\sqrt{[}(2 \mathrm{GM}) / \mathrm{R}]\) (B) \(2 \sqrt{(\mathrm{GM} / \mathrm{R})}\) (C) \(\sqrt{[}(2 \mathrm{GMm}) / \mathrm{R}]\) (D) \(\sqrt{(\mathrm{GM} / \mathrm{R})}\)

Two bodies of masses \(m_{1}\) and \(m_{2}\) are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual a gravitational attraction Their relative velocity of approach at separation distance \(\mathrm{r}\) between them is (A) $\left[\left\\{2 \mathrm{G}\left(\mathrm{m}_{1}-\mathrm{m}_{2}\right)\right\\} / \mathrm{r}\right]^{-1 / 2}$ (B) $\left[\left\\{2 \mathrm{G}\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right)\right\\} / \mathrm{r}\right]^{1 / 2}$ (C) $\left[\mathrm{r} /\left\\{2 \mathrm{G}\left(\mathrm{m}_{1} \mathrm{~m}_{2}\right)\right\\} / \mathrm{r}\right]^{1 / 2}$ (D) $\left[\left(2 \mathrm{Gm}_{1} \mathrm{~m}_{2}\right) / \mathrm{r}\right]^{1 / 2}$

The mass and radius of the sun are \(1.99 \times 10^{30} \mathrm{~kg}\) and \(\mathrm{R}=6.96 \times 10^{8} \mathrm{~m}\). The escape velocity of rocket from the sun \(\mathrm{is}=\ldots \ldots \ldots \mathrm{km} / \mathrm{sec}\) $\begin{array}{llll}\text { (A } 11.2 & \text { (B) } 12.38 & \text { (C) } 59.5 & \text { (D) } 618\end{array}$

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to four times the previous value, the new time period will become \(\ldots \ldots \ldots\) hours (A) 10 (B) 120 (C) 40 (D) 80

Escape velocity on the surface of earth is \(11.2 \mathrm{kms}^{-1}\) Escape velocity from a planet whose masses the same as that of earth and radius $1 / 4\( that of earth is \)=\ldots \ldots \ldots \mathrm{kms}^{-1}$ (A) \(2.8\) (B) \(15.6\) (C) \(22.4\) (D) \(44.8\)
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