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If the time period of a planet is increased to 3√3 times its present value, the percentage increase in its radius of the orbit of revolution will be ?
Most Upvoted Answer
If the time period of a planet is increased to 3√3 times its present v...
Calculation of Percentage Increase in Radius of Orbit
- Let's assume the initial time period of the planet's revolution is T and its initial radius of orbit is R.
- According to Kepler's third law, T^2 is directly proportional to R^3.
Given:
- If the time period is increased to 3√3 times its present value, the new time period will be 3√3T.
- We need to find the percentage increase in the radius of the orbit.
Calculations:
- Initial relation: T^2 ∝ R^3
- New relation: (3√3T)^2 ∝ (R + ΔR)^3, where ΔR is the change in the radius of the orbit.
- (3√3T)^2 = 9 * 3 * T^2 = 27T^2
- (R + ΔR)^3 = R^3 * (1 + ΔR/R)^3
- 27T^2 = R^3 * (1 + ΔR/R)^3
- Taking cube root on both sides,
- 3√27T = R * (1 + ΔR/R)
- 3√27 * T = R + ΔR
Percentage Increase in Radius:
- Percentage increase = (ΔR / R) * 100
- Percentage increase = ((3√27 * T) - R) / R * 100
Final Answer:
- By calculating the above expression, we can find the percentage increase in the radius of the orbit of revolution when the time period is increased to 3√3 times its present value.
- Let's assume the initial time period of the planet's revolution is T and its initial radius of orbit is R.
- According to Kepler's third law, T^2 is directly proportional to R^3.
Given:
- If the time period is increased to 3√3 times its present value, the new time period will be 3√3T.
- We need to find the percentage increase in the radius of the orbit.
Calculations:
- Initial relation: T^2 ∝ R^3
- New relation: (3√3T)^2 ∝ (R + ΔR)^3, where ΔR is the change in the radius of the orbit.
- (3√3T)^2 = 9 * 3 * T^2 = 27T^2
- (R + ΔR)^3 = R^3 * (1 + ΔR/R)^3
- 27T^2 = R^3 * (1 + ΔR/R)^3
- Taking cube root on both sides,
- 3√27T = R * (1 + ΔR/R)
- 3√27 * T = R + ΔR
Percentage Increase in Radius:
- Percentage increase = (ΔR / R) * 100
- Percentage increase = ((3√27 * T) - R) / R * 100
Final Answer:
- By calculating the above expression, we can find the percentage increase in the radius of the orbit of revolution when the time period is increased to 3√3 times its present value.
Community Answer
If the time period of a planet is increased to 3√3 times its present v...
T2 is directly proportional to r3
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If the time period of a planet is increased to 3√3 times its present value, the percentage increase in its radius of the orbit of revolution will be ?
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If the time period of a planet is increased to 3√3 times its present value, the percentage increase in its radius of the orbit of revolution will be ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the time period of a planet is increased to 3√3 times its present value, the percentage increase in its radius of the orbit of revolution will be ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the time period of a planet is increased to 3√3 times its present value, the percentage increase in its radius of the orbit of revolution will be ?.
If the time period of a planet is increased to 3√3 times its present value, the percentage increase in its radius of the orbit of revolution will be ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the time period of a planet is increased to 3√3 times its present value, the percentage increase in its radius of the orbit of revolution will be ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the time period of a planet is increased to 3√3 times its present value, the percentage increase in its radius of the orbit of revolution will be ?.
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