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The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3 V, then the speed of satellite B will be: [2010]
- a)3 V/4
- b)6 V
- c)12 V
- d)3 V/2
Correct answer is option 'B'. Can you explain this answer?
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Solution:
Given:
- The radii of circular orbits of two satellites A and B of the earth are 4R and R respectively.
- The speed of satellite A is 3V.
To find:
- The speed of satellite B.
Explanation:
The speed of an object in a circular orbit is given by the equation:
speed = (2πr) / T
where:
- speed is the speed of the object in the orbit
- r is the radius of the orbit
- T is the time period of the orbit
Step 1: Finding the time period of satellite A
Since the speed of satellite A is 3V and its radius is 4R, we can find the time period using the equation above:
3V = (2π * 4R) / T
Step 2: Finding the time period of satellite B
Since the radius of satellite B is R, we can find its time period using the equation above:
speed of satellite B = (2π * R) / T
Step 3: Comparing the time periods of satellite A and B
From step 1, we have the time period of satellite A as T.
From step 2, we have the time period of satellite B as T.
Since the time period is the same for both satellites, we can conclude that the speed of satellite B is the same as the speed of satellite A.
Therefore, the speed of satellite B is 3V.
Hence, the correct answer is option B.
Given:
- The radii of circular orbits of two satellites A and B of the earth are 4R and R respectively.
- The speed of satellite A is 3V.
To find:
- The speed of satellite B.
Explanation:
The speed of an object in a circular orbit is given by the equation:
speed = (2πr) / T
where:
- speed is the speed of the object in the orbit
- r is the radius of the orbit
- T is the time period of the orbit
Step 1: Finding the time period of satellite A
Since the speed of satellite A is 3V and its radius is 4R, we can find the time period using the equation above:
3V = (2π * 4R) / T
Step 2: Finding the time period of satellite B
Since the radius of satellite B is R, we can find its time period using the equation above:
speed of satellite B = (2π * R) / T
Step 3: Comparing the time periods of satellite A and B
From step 1, we have the time period of satellite A as T.
From step 2, we have the time period of satellite B as T.
Since the time period is the same for both satellites, we can conclude that the speed of satellite B is the same as the speed of satellite A.
Therefore, the speed of satellite B is 3V.
Hence, the correct answer is option B.
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The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3 V, then the speed of satellite B will be: [2010]a)3 V/4b)6 Vc)12 Vd)3 V/2Correct answer is option 'B'. Can you explain this answer?
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