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Two small satellies move in a circular o...

Two small satellies move in a circular orbits around the earth, at disatnce `r` and `(r + dr)` from the centre of the earth. Their time periods of rotation ate `T` and `T + dT (Delta r lt lt b r, DeltaT lt lt T)`. Then

A

`DeltaT = (3)/(2)T (Delta r)/(r )`

B

`DeltaT = (-3)/(2)T (Delta r)/(r )`

C

`DeltaT = (2)/(3)T (Delta r)/(r )`

D

`DeltaT = T (Delta r)/(r )`

Text Solution

Verified by Experts

The correct Answer is:
A
As `T^(2) prop r^(3)` or `T^(2) = Kr^(3)` ..(i)
Differentating it, we have
`2T Delta T = 3Kr^(2) Delta r` ..(ii)
Dividing (ii) by (i), we have
`(2T DeltaT)/(T^(2)) = (3kr^(2)Delta r)/(Kr^(3))` or `DeltaT = (3)/(2)T (Delta r)/(r )`
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