A t what angular speed should the earth rotate so that a body situated on the equator becomes weightless ?
( Acceleration due to gravity = 9.8 $m / s^{2}$ , Radius of the earth = 6400 km)

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Solution

For weightless condition.
$\begin{matrix} m g = m R_{e} w^{2} {cos}^{2} λ w = \sqrt{\frac{g}{R_{e}}} = \frac{1}{800} \end{matrix}$
$= 1.25 \times 10^{- 3} r a d / s$
At equation,
$λ = 0$

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A t what angular speed should the earth rotate so that a body situated on the equator becomes weightless ? ( Acceleration due to gravity = 9.8 m/s2 , Radius of the earth = 6400 km)

For weightless condition.mg=mRew2cos2λw=√gRe=1800=1.25×10−3rad/sAt equation,λ=0

A t what angular speed should the earth rotate so that a body situated on the equator becomes weightless ?
( Acceleration due to gravity = 9.8 $m / s^{2}$ , Radius of the earth = 6400 km)

For weightless condition.
$\begin{matrix} m g = m R_{e} w^{2} {cos}^{2} λ w = \sqrt{\frac{g}{R_{e}}} = \frac{1}{800} \end{matrix}$
$= 1.25 \times 10^{- 3} r a d / s$
At equation,
$λ = 0$