Q.

A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed (v0). Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If R = radius of the Earth and ω be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.

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a

4πωR2v02+R2ω2

b

2πωR2v02−R2ω2

c

4πωR2v02−R2ω2

d

2πωR2v02+R2ω2

answer is C.

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Detailed Solution

Twest =2πRv0+Rω and Teast =2πRv0−Rω⇒⇒∆T=Teast −Twest =2πRV0-Rω-2πRV0+Rω=2πR×2Rωv02−R2ω2=4πωR2v02−R2ω2
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