Question

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately:
(Take: $g =10\,ms ^{-2}$, the radius of earth, $R =6400 \times 10^{3} m$, Take $\left.\pi=3.14\right)$

• A. 60 minutes
• B. does not change
• C. 1200 minutes
• D. 84 minutes

Answer 1

Answer: (D)

For objects to float
$mg = m \omega^{2} R$
$\omega=$ angular velocity of earth. $R =$ Radius of earth
$\omega=\sqrt{\frac{g}{R}}\,\,\,\,\,\dots(1)$
Duration of day $= T$
$T =\frac{2 \pi}{\omega}\,\,\,\,\dots(2)$
$\Rightarrow T =2 \pi \sqrt{\frac{ R }{ g }}$
$=2 \pi \sqrt{\frac{6400 \times 10^{3}}{10}}$
$\Rightarrow \frac{ T }{60}=83.775$ minutes
$=84$ minutes