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7.Gravitation
hard
The acceleration due to gravity on the earth's surface at the poles is $g$ and angular velocity of the earth about the axis passing through the pole is $\omega .$ An object is weighed at the equator and at a height $h$ above the poles by using a spring balance. If the weights are found to be same, then $h$ is $:( h << R ,$ where $R$ is the radius of the earth)
A
$\frac{ R ^{2} \omega^{2}}{8 g }$
B
$\frac{ R ^{2} \omega^{2}}{4 g }$
C
$\frac{ R ^{2} \omega^{2}}{ g }$
D
$\frac{ R ^{2} \omega^{2}}{2 g }$
(JEE MAIN-2020)
Solution
$g _{ e }= g – R \omega^{2}$
$g_{2}=g\left(1-\frac{2 h}{R}\right)$
$g_{2}=g-\frac{2 g h}{R}$
Now $R \omega^{2}=\frac{2 g h}{R}$
$h=\frac{R^{2} \omega^{2}}{2 g}$
Standard 11
Physics
