Question 173: Gravitation

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 = 10 ms$$-$$2, the radius of earth, R = 6400 $$	imes$$ 103 m, Take $$\pi$$ = 3.14]

Accepted Answer

For objects to float
mg = 2$$\omega$$
2
R
$$\omega$$ = angular velocity of earth.
R = Radius of earth
$$\omega  = \sqrt {{g \over R}} $$ ..... (1)
Duration of day = T
$$T = {{2\pi } \over \omega }$$ ..... (2)
$$ \Rightarrow T = 2\pi \sqrt {{R \over g}} $$
$$ = 2\pi \sqrt {{{6400 	imes {{10}^3}} \over {10}}} $$
$$ \Rightarrow {T \over {60}}$$ = 83.775 minutes
$$ \simeq $$ 84 minuites

Answer

84 minutes

Answer

1200 minutes

Answer

60 minutes

Answer

does not change

Gravitation

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]

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