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A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly by
- a)2 times
- b)2.5 times
- c)2.8 times
- d)3.2 times
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A satellite orbiting around the earth of radius R is shifted to an orb...
The time period of a satellite orbiting around the earth is
When the radius of the orbit is increased to 2R
T' = 2 × 1.414 T
T' = 2.828 T ≈ 2.8 T
When the radius of the orbit is increased to 2R
T' = 2 × 1.414 T
T' = 2.828 T ≈ 2.8 T
Most Upvoted Answer
A satellite orbiting around the earth of radius R is shifted to an orb...
Solution:
Given, a satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R.
Let T1 be the time period of the satellite when it is orbiting at radius R and T2 be the time period of the satellite when it is orbiting at radius 2R.
We know that time period of a satellite is given by,
T = 2π √(r^3/GM)
Where,
r = radius of the orbit
G = Gravitational constant
M = Mass of the earth
Now, let's calculate the time period T1 when the satellite is orbiting at radius R,
T1 = 2π √(R^3/GM) ----(1)
Similarly, let's calculate the time period T2 when the satellite is orbiting at radius 2R,
T2 = 2π √((2R)^3/GM)
T2 = 2π √(8R^3/GM)
T2 = 2π √(8(R^3/GM))
T2 = 2π √(8T1)
T2 = 2π * 2√2 * √T1
T2 = 2.83T1
Therefore, the time taken for one revolution will increase nearly by 2.83 times.
Hence, the correct option is (c) 2.8 times.
Given, a satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R.
Let T1 be the time period of the satellite when it is orbiting at radius R and T2 be the time period of the satellite when it is orbiting at radius 2R.
We know that time period of a satellite is given by,
T = 2π √(r^3/GM)
Where,
r = radius of the orbit
G = Gravitational constant
M = Mass of the earth
Now, let's calculate the time period T1 when the satellite is orbiting at radius R,
T1 = 2π √(R^3/GM) ----(1)
Similarly, let's calculate the time period T2 when the satellite is orbiting at radius 2R,
T2 = 2π √((2R)^3/GM)
T2 = 2π √(8R^3/GM)
T2 = 2π √(8(R^3/GM))
T2 = 2π √(8T1)
T2 = 2π * 2√2 * √T1
T2 = 2.83T1
Therefore, the time taken for one revolution will increase nearly by 2.83 times.
Hence, the correct option is (c) 2.8 times.
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A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly bya)2 timesb)2.5 timesc)2.8 timesd)3.2 timesCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly bya)2 timesb)2.5 timesc)2.8 timesd)3.2 timesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly bya)2 timesb)2.5 timesc)2.8 timesd)3.2 timesCorrect answer is option 'C'. Can you explain this answer?.
A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly bya)2 timesb)2.5 timesc)2.8 timesd)3.2 timesCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly bya)2 timesb)2.5 timesc)2.8 timesd)3.2 timesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly bya)2 timesb)2.5 timesc)2.8 timesd)3.2 timesCorrect answer is option 'C'. Can you explain this answer?.
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