If angular velocity of earth's spin is increased such that bodies at equator start floating

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7.Gravitation

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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

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