SATHEE: Gravitation Question 227

Gravitation Question 227

Question:A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed ( $[v_{0}]$ ). 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.

Options:

A) $[\frac{4 π ω R^{2}}{v_{0}^{2} + R^{2} ω^{2}}]$

B) $[\frac{2 π ω R^{2}}{v_{0}^{2} - R^{2} ω^{2}}]$

C) $[\frac{4 π ω R^{2}}{v_{0}^{2} - R^{2} ω^{2}}]$

D) $[\frac{2 π ω R^{2}}{v_{0}^{2} + R^{2} ω^{2}}]$

Show Answer

Answer:

Correct Answer: C

Solution:

$[T_{w e s t} = \frac{2 π R}{v_{0} + R ω}]$ and $[T_{e a s t} = \frac{2 π R}{v_{0} - R ω} \Rightarrow Δ T = T_{e a s t}]$ $[\Rightarrow T_{e a s t} - T_{w e s t} = 2 π R [\frac{2 π R}{v_{0}^{2} - R^{2} ω^{2}}] = \frac{4 π ω R^{2}}{v_{0}^{2} - R^{2} ω^{2}}]$

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Gravitation Question 227

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