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Question
Answer the following question in detail.
Two satellites A and B are revolving round a planet. Their periods of revolution are 1 hour and 8 hour respectively. The radius of orbit of satellite B is 4 × 104 km. Find radius of orbit of satellite A.
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Solution
Given: TA = 1 hour, TB = 8 hour, rB = 4 × 104 km
To find: Radius of orbit of satellite A (rA)
Formula: T = `2pi sqrt("r"^3/"GM")`
Calculation: From formula,
`"T"^2 = (4pi^2"r"^3)/"GM"`
∴ `"T"^2 prop "r"^3 ......(because (4pi^2"r"^3)/"GM" = "constant for a planet")`
∴ `(("T"_"A")/("T"_"B"))^2 = (("r"_"A")/("r"_"B"))^3`
∴ `(1/8)^2 = ("r"_"A"/(4 xx 10^4))^3`
∴ `"r"_"A"^3 = 1/(8)^2 xx (4 xx 10^4)^3`
∴ `"r"_"A"^3 = 10^12`
∴ `"r"_"A" = 1 xx 10^4` km
Radius of orbit of satellite A will be 1 × 104 km.
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