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<
Correct Option: , 2
(2) Value of $g$ at equator, $g_{A}=g \cdot-R \omega^{2}$
Value of $g$ at height $h$ above the pole,
$g_{B}=g \cdot\left(1-\frac{2 h}{R}\right)$
As object is weighed equally at the equator and poles, it means $g$ is same at these places.
$g_{A}=g_{B}$
$\Rightarrow g-R \omega^{2}=g\left(1-\frac{2 h}{R}\right)$
$\Rightarrow R \omega^{2}=\frac{2 g h}{R} \Rightarrow h=\frac{R^{2} \omega^{2}}{2 g}$
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