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7.Gravitation
medium
The rotation of the earth having radius $R$ about its axis speeds upto a value such that a man at latitude angle $60^{\circ}$ feels weightless. The duration of the day in such case will be:
A
$8 \pi \sqrt{\frac{ R }{ g }}$
B
$8 \pi \sqrt{\frac{g}{R}}$
C
$\pi \sqrt{\frac{R}{g}}$
D
$4 \pi \sqrt{\frac{g}{R}}$
Solution
(c)
$0=g-R \omega ^2 \cos ^2 60^{\circ}$
$\omega ^2=\frac{4 g}{R}$
$\omega ^2=2 \sqrt{\frac{g}{R}}$
$\frac{2 \pi}{T}=2 \sqrt{\frac{g}{R}}$
$T=\pi \sqrt{\frac{R}{g}}$
Standard 11
Physics
