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7.Gravitation
normal
The rotation of the earth having $R$ radius about its axis speeds up to a value such that a man at latitude angle $60^o$ feels weightlessness. The duration of the day in such a case is.
A
$2 \pi \sqrt{\frac{R}{g}}$
B
$ \pi \sqrt{\frac{R}{g}}$
C
$2 \pi \sqrt{\frac{g}{R}}$
D
$4 \pi \sqrt{\frac{R}{g}}$
Solution
$0=\mathrm{g}-\mathrm{R} \omega^{2} \cos ^{2} 60^{\circ}$
$\Rightarrow \frac{\mathrm{R}^{2} \omega^{2}}{4}=\mathrm{g} \quad \Rightarrow \omega=2 \sqrt{\frac{\mathrm{g}}{\mathrm{R}}}$
$\Rightarrow \mathrm{T}=4 \pi \sqrt{\frac{\mathrm{R}}{\mathrm{g}}}$
Standard 11
Physics
