The acceleration due to gravity on the earth’s surface at the poles… | JEE Main 2020 (5 Sep, Shift 2)

Q107JEE Main 2020 · 5 SEP · SHIFT 2Difficult

Acceleration Due to Gravity

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)

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Answer: (a)

At the equator: $W_1 = m(g - \omega^2 R)$
At height $h$ above the pole ( $h \ll R$ ): $W_2 = mg\left(1 - \frac{2h}{R}\right)$
$W_1 = W_2 \Rightarrow \omega^2 R = \frac{2gh}{R}$
$h = \frac{R^2\omega^2}{2g}$ , so the answer is (a).

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