If the angular velocity of earth's spin is increased such that the bodies at the

(4)

For objects to float

$\mathrm{mg}=\mathrm{m} \omega^{2} \mathrm{R}$

$\omega=$ angular velocity of earth.

$\mathrm{R}=$ Radius of earth

$\omega=\sqrt{\frac{g}{R}} \ldots(1)$

Duration of day $=\mathrm{T}$

$\mathrm{T}=\frac{2 \pi}{\omega} \ldots(2)$

$\Rightarrow \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{R}}{\mathrm{g}}}$

$=2 \pi \sqrt{\frac{6400 \times 10^{3}}{10}}$

$\Rightarrow \frac{\mathrm{T}}{60}=83.775$ minutes

$\simeq 84$ minutes