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With what speed the earth should rotate ...

With what speed the earth should rotate about its own axis so that a person should weigh at the equator `(3)/(5)`th of his weight at persent? (Take R = 6400 km):

A

`7.83" rad s"^(-1)`

B

`1.25xx10^(-4)" rad s"^(-1)`

C

`7.83xx10^(-4)" rad s"^(-1)`

D

none of the above.

Text Solution

Verified by Experts

The correct Answer is:
C
Here `mRomega^(2)=mg-(3)/(5)mg =(2)/(5)mg`
`omega=((2g)/(5R))^((1)/(2))=((2xx9.8)/(5xx6.4xx10^(6)))^((1)/(2))=7.83xx10^(-4)`rad/sec.
Thus the correct choice is (c ).
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