JEE MAIN - Physics (2021 - 18th March Evening Shift - No. 2)
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 $$\times$$ 103 m, Take $$\pi$$ = 3.14]
84 minutes
1200 minutes
60 minutes
does not change
Explanation
For objects to float
mg = 2$$\omega$$2R
$$\omega$$ = angular velocity of earth.
R = Radius of earth
$$\omega = \sqrt {{g \over R}} $$ ..... (1)
Duration of day = T
$$T = {{2\pi } \over \omega }$$ ..... (2)
$$ \Rightarrow T = 2\pi \sqrt {{R \over g}} $$
$$ = 2\pi \sqrt {{{6400 \times {{10}^3}} \over {10}}} $$
$$ \Rightarrow {T \over {60}}$$ = 83.775 minutes
$$ \simeq $$ 84 minuites
mg = 2$$\omega$$2R
$$\omega$$ = angular velocity of earth.
R = Radius of earth
$$\omega = \sqrt {{g \over R}} $$ ..... (1)
Duration of day = T
$$T = {{2\pi } \over \omega }$$ ..... (2)
$$ \Rightarrow T = 2\pi \sqrt {{R \over g}} $$
$$ = 2\pi \sqrt {{{6400 \times {{10}^3}} \over {10}}} $$
$$ \Rightarrow {T \over {60}}$$ = 83.775 minutes
$$ \simeq $$ 84 minuites
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