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The rotation of the earth having \mathrm{R} radius about its axis speeds up to a value such that a man at latitude angle  \mathrm{60^{\circ}} feels weightlessness. The duration of the day in such a case is.
 

Option: 1

\mathrm{2 \pi \sqrt{\frac{R}{g}}}

 


Option: 2

\mathrm{\quad 4 \pi \sqrt{\frac{R}{g}}}

 


Option: 3

\mathrm{2 \pi \sqrt{\frac{g}{R}}}
 


Option: 4

\mathrm{\quad 4 \pi \sqrt{\frac{g}{R}}}


Answers (1)

best_answer

\mathrm{ 0=g-R \omega^2 \cos ^2 60^{\circ} }

\mathrm{ \Rightarrow \frac{R^2 \omega^2}{4}=g }

\mathrm{ \Rightarrow \omega=2 \sqrt{\frac{g}{R}} }

\mathrm{ \Rightarrow T=4 \pi \sqrt{\frac{R}{g}} }

Hence option 2 is correct.


 

Posted by

Anam Khan

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