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Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:
Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.
Reason : Greater the height above the earth’s surface, greater is the time period of revolution.
- a)Both assertion and reason are true and reason is the correct explanation of assertion.
- b)Both assertion and reason are true but reason is not the correct explanation of assertion.
- c)Assertion is true but reason is false.
- d)Both Assertion and Reason are false.
Correct answer is option 'B'. Can you explain this answer?
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Direction : In each of the following questions, a statement of Assert...
According to Kepler’s law, T2 ∝ r3 or T ∝ r3/2
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When r becomes four times, T is 43/2 (= 23) = 8 times.
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Direction : In each of the following questions, a statement of Assert...
Assertion: When the orbital radius of a planet is made 4 times, its time period increases by 8 times.
Reason: Greater the height above the earth’s surface, greater is the time period of revolution.
Explanation:
The assertion states that when the orbital radius of a planet is made 4 times, its time period increases by 8 times. To understand this, we need to analyze the relationship between the orbital radius and the time period of a planet.
The Relationship Between Orbital Radius and Time Period:
The time period of a planet is the time it takes for the planet to complete one revolution around the sun. The orbital radius of a planet is the average distance between the planet and the sun.
Kepler’s Third Law of Planetary Motion states that the square of the time period of a planet is directly proportional to the cube of its orbital radius. Mathematically, it can be represented as:
T^2 ∝ R^3
Where T is the time period and R is the orbital radius.
Let's consider an example to understand the relationship. Suppose we have a planet with an orbital radius of R and a time period of T. According to Kepler’s Third Law, we have:
T^2 ∝ R^3
Now, if we make the orbital radius 4 times its original value, it becomes 4R. According to the relationship, the new time period, let's call it T', will be:
T'^2 ∝ (4R)^3
T'^2 ∝ 64R^3
Comparing this with the original relationship, we can see that the new time period is 64 times the original time period:
T' = √(64R^3)
T' = 8√(R^3)
T' = 8R√R
Therefore, the assertion is correct. When the orbital radius of a planet is made 4 times, its time period increases by 8 times.
Now, let's analyze the reason given in the statement. The reason states that the greater the height above the earth’s surface, the greater is the time period of revolution. This is true because as the height above the earth’s surface increases, the orbital radius of the planet increases. And according to Kepler’s Third Law, an increase in the orbital radius leads to an increase in the time period of revolution.
However, it is important to note that the reason alone does not explain why the time period increases by 8 times when the orbital radius is made 4 times. The reason only explains the relationship between the height above the earth’s surface and the time period of revolution, but not the specific ratio of increase in the time period when the orbital radius is changed.
Therefore, both the assertion and reason are true, but the reason is not the correct explanation of the assertion. Hence, the correct answer is option B.
Reason: Greater the height above the earth’s surface, greater is the time period of revolution.
Explanation:
The assertion states that when the orbital radius of a planet is made 4 times, its time period increases by 8 times. To understand this, we need to analyze the relationship between the orbital radius and the time period of a planet.
The Relationship Between Orbital Radius and Time Period:
The time period of a planet is the time it takes for the planet to complete one revolution around the sun. The orbital radius of a planet is the average distance between the planet and the sun.
Kepler’s Third Law of Planetary Motion states that the square of the time period of a planet is directly proportional to the cube of its orbital radius. Mathematically, it can be represented as:
T^2 ∝ R^3
Where T is the time period and R is the orbital radius.
Let's consider an example to understand the relationship. Suppose we have a planet with an orbital radius of R and a time period of T. According to Kepler’s Third Law, we have:
T^2 ∝ R^3
Now, if we make the orbital radius 4 times its original value, it becomes 4R. According to the relationship, the new time period, let's call it T', will be:
T'^2 ∝ (4R)^3
T'^2 ∝ 64R^3
Comparing this with the original relationship, we can see that the new time period is 64 times the original time period:
T' = √(64R^3)
T' = 8√(R^3)
T' = 8R√R
Therefore, the assertion is correct. When the orbital radius of a planet is made 4 times, its time period increases by 8 times.
Now, let's analyze the reason given in the statement. The reason states that the greater the height above the earth’s surface, the greater is the time period of revolution. This is true because as the height above the earth’s surface increases, the orbital radius of the planet increases. And according to Kepler’s Third Law, an increase in the orbital radius leads to an increase in the time period of revolution.
However, it is important to note that the reason alone does not explain why the time period increases by 8 times when the orbital radius is made 4 times. The reason only explains the relationship between the height above the earth’s surface and the time period of revolution, but not the specific ratio of increase in the time period when the orbital radius is changed.
Therefore, both the assertion and reason are true, but the reason is not the correct explanation of the assertion. Hence, the correct answer is option B.
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Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer?
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Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer?.
Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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ample number of questions to practice Direction : In each of the following questions, a statement of Assertion is given and a corresponding statement of Reason is given just below it. Of the statements, given below, mark the correct answer as:Assertion : When the orbital radius of a planet is made 4 times, its time period increases by 8 times.Reason : Greater the height above the earth’s surface, greater is the time period of revolution.a)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Both Assertion and Reason are false.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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