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Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. their periods of revolution are 1h and 8h respectively. The radius of the orbit of S1 is 10 to the power 4 km. When S2 is closest to S1, find (a)the speed of S2 relative to S1 and (b) the angular speed of S2 as observed by an astronaut in S1.?
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Two satellites S1 and S2 revolve round a planet in coplanar circular o...
Given:
- Radius of the orbit of S1: 10^4 km
- Period of revolution of S1: 1 hour
- Period of revolution of S2: 8 hours
To Find:
(a) The speed of S2 relative to S1
(b) The angular speed of S2 as observed by an astronaut in S1
Solution:
1. Speed of S1:
The speed of an object in circular motion can be calculated using the formula:
Speed = 2πr / T
where r is the radius of the orbit and T is the period of revolution.
Substituting the given values:
Speed of S1 = 2π(10^4 km) / 1 hour = 20π(10^4) km/h
2. Speed of S2:
Since S1 and S2 are revolving in the same sense, the relative speed of S2 with respect to S1 can be calculated by subtracting the speed of S1 from the speed of S2.
Relative Speed of S2 = Speed of S2 - Speed of S1
We know that the time period of S2 is 8 hours. Using the formula mentioned above, we can find the speed of S2.
Speed of S2 = 2πr / T = 2π(10^4 km) / 8 hours = π(10^4) / 4 km/h
Now, substituting the values in the relative speed formula:
Relative Speed of S2 = π(10^4) / 4 km/h - 20π(10^4) km/h
Simplifying the expression:
Relative Speed of S2 = (π(10^4) - 80π(10^4)) km/h = -79π(10^4) km/h
Therefore, the speed of S2 relative to S1 is -79π(10^4) km/h.
3. Angular Speed of S2:
The angular speed of S2 as observed by an astronaut in S1 can be calculated using the formula:
Angular Speed = 2π / T
where T is the period of revolution.
Substituting the given value:
Angular Speed of S2 = 2π / 8 hours = π / 4 radians per hour
Therefore, the angular speed of S2 as observed by an astronaut in S1 is π / 4 radians per hour.
- Radius of the orbit of S1: 10^4 km
- Period of revolution of S1: 1 hour
- Period of revolution of S2: 8 hours
To Find:
(a) The speed of S2 relative to S1
(b) The angular speed of S2 as observed by an astronaut in S1
Solution:
1. Speed of S1:
The speed of an object in circular motion can be calculated using the formula:
Speed = 2πr / T
where r is the radius of the orbit and T is the period of revolution.
Substituting the given values:
Speed of S1 = 2π(10^4 km) / 1 hour = 20π(10^4) km/h
2. Speed of S2:
Since S1 and S2 are revolving in the same sense, the relative speed of S2 with respect to S1 can be calculated by subtracting the speed of S1 from the speed of S2.
Relative Speed of S2 = Speed of S2 - Speed of S1
We know that the time period of S2 is 8 hours. Using the formula mentioned above, we can find the speed of S2.
Speed of S2 = 2πr / T = 2π(10^4 km) / 8 hours = π(10^4) / 4 km/h
Now, substituting the values in the relative speed formula:
Relative Speed of S2 = π(10^4) / 4 km/h - 20π(10^4) km/h
Simplifying the expression:
Relative Speed of S2 = (π(10^4) - 80π(10^4)) km/h = -79π(10^4) km/h
Therefore, the speed of S2 relative to S1 is -79π(10^4) km/h.
3. Angular Speed of S2:
The angular speed of S2 as observed by an astronaut in S1 can be calculated using the formula:
Angular Speed = 2π / T
where T is the period of revolution.
Substituting the given value:
Angular Speed of S2 = 2π / 8 hours = π / 4 radians per hour
Therefore, the angular speed of S2 as observed by an astronaut in S1 is π / 4 radians per hour.
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Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. their periods of revolution are 1h and 8h respectively. The radius of the orbit of S1 is 10 to the power 4 km. When S2 is closest to S1, find (a)the speed of S2 relative to S1 and (b) the angular speed of S2 as observed by an astronaut in S1.?
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Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. their periods of revolution are 1h and 8h respectively. The radius of the orbit of S1 is 10 to the power 4 km. When S2 is closest to S1, find (a)the speed of S2 relative to S1 and (b) the angular speed of S2 as observed by an astronaut in S1.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. their periods of revolution are 1h and 8h respectively. The radius of the orbit of S1 is 10 to the power 4 km. When S2 is closest to S1, find (a)the speed of S2 relative to S1 and (b) the angular speed of S2 as observed by an astronaut in S1.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. their periods of revolution are 1h and 8h respectively. The radius of the orbit of S1 is 10 to the power 4 km. When S2 is closest to S1, find (a)the speed of S2 relative to S1 and (b) the angular speed of S2 as observed by an astronaut in S1.?.
Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. their periods of revolution are 1h and 8h respectively. The radius of the orbit of S1 is 10 to the power 4 km. When S2 is closest to S1, find (a)the speed of S2 relative to S1 and (b) the angular speed of S2 as observed by an astronaut in S1.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. their periods of revolution are 1h and 8h respectively. The radius of the orbit of S1 is 10 to the power 4 km. When S2 is closest to S1, find (a)the speed of S2 relative to S1 and (b) the angular speed of S2 as observed by an astronaut in S1.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. their periods of revolution are 1h and 8h respectively. The radius of the orbit of S1 is 10 to the power 4 km. When S2 is closest to S1, find (a)the speed of S2 relative to S1 and (b) the angular speed of S2 as observed by an astronaut in S1.?.
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