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: $g=10m{s}^{-2}$, the radius of earth, $R=6400\times 10^{3}m$, Take $\pi =3.14)$

• 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