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In the above example the angular velocit...

In the above example the angular velocity of `S_(2)` as actually observed by an astronaut in `S_(1)` is -

A

`3xx10^(-4)`

B

`3xx10^(23)`

C

`3xx10^(-6)`

D

`3xx10^(-7)`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Angular speed of `S_(2)` as observed by astronaut in `S_(1)`.
`omega_(r )=(|v_(1)-v_(2)|)/(|r_(2)-r_(1)|)`
`|v_(1)-v_(2)|=(2pixx10^(4)-pixx10^(4))km//h`
`or |v_(1)-v_(2)|=(pixx10^(4)xx1000)/(60xx60)m//s`
`or |v_(1)-v_(2)|=(3.14xx10^(5))/(36)=0.0872xx10^(5)=8.72xx10^(3) m//s`
`|r_(2)-r_(1)|=3xx10^(7) m`
`:. omega_(r )=(8.72xx10^(3))/(3xx10^(7))=2.9xx10^(-4)~~3xx10^(-4) rad//sec`
`:. omega_(r )=3xx10^(-4) rad//sec.`
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