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7.Gravitation
medium
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 ........ minutes
(Take : $g =10 \,ms ^{-2},$ the radius of earth, $R =6400 \times 10^{3}\, m ,$ Take $\left.\pi=3.14\right)$
A
$60$
B
$480$
C
$1200$
D
$84$
(JEE MAIN-2021)
Solution
For objects to float
$mg = m \omega^{2} R$
$\omega=$ angular velocity of earth.
$R =$ Radius of earth
$\omega=\sqrt{\frac{g}{R}}$
Duration of day $= T$
$T =\frac{2 \pi}{\omega}$
$\Rightarrow T =2 \pi \sqrt{\frac{ R }{ g }}$
$=2 \pi \sqrt{\frac{6400 \times 10^{3}}{10}}$
$\Rightarrow \frac{ T }{60}=83.775$ minutes
$\simeq 84$ minutes
Standard 11
Physics
