Identical packets are dropped from two airplanes, one above the equator and the other above the north pole, both at height $h$ . Assuming all conditions are identical, will those packets take the same time to reach the surface of the earth. Justify your answer.

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Solution

Comparison between gravity at poles and at equator:
Gravity at Poles
Gravity at Equator
1. Due to the oblate spheroid shape of the earth, both poles are flattened out. 1. Due to the oblate spheroid shape of the earth the equator bulges out.
2. Hence, poles are closer to the center of the earth. 2. Hence, the equator is further away from the center of the earth.
3. The value of $g = \frac{G M}{R^{2}}$ and $R_{P} < R_{E}$ , therefore, gravity at the poles is greater. 3. The value of $g = \frac{G M}{R^{2}}$ and $R_{P} < R_{E}$ , therefore, gravity at the equator is lesser.
4. The third equation of motion states that, $v^{2} = u^{2} + 2 g h$ , so for higher value of $g$ the velocity will be more. 4. The third equation of motion states that, $v^{2} = u^{2} + 2 g h$ , so for lower value of $g$ the velocity will be less.
5. So, the packet dropped from height $h$ above the poles will take less time to reach the surface of the earth. 5. So, the packet dropped from height $h$ above the equator will take more time to reach the surface of the earth.
Hence, identical packets are dropped from two airplanes from height $h$ , the packet at the poles will take less time than the packet at the equator to reach the surface of the earth.

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Gravity at Poles	Gravity at Equator
1. Due to the oblate spheroid shape of the earth, both poles are flattened out.	1. Due to the oblate spheroid shape of the earth the equator bulges out.
2. Hence, poles are closer to the center of the earth.	2. Hence, the equator is further away from the center of the earth.
3. The value of $g = \frac{G M}{R^{2}}$ and $R_{P} < R_{E}$ , therefore, gravity at the poles is greater.	3. The value of $g = \frac{G M}{R^{2}}$ and $R_{P} < R_{E}$ , therefore, gravity at the equator is lesser.
4. The third equation of motion states that, $v^{2} = u^{2} + 2 g h$ , so for higher value of $g$ the velocity will be more.	4. The third equation of motion states that, $v^{2} = u^{2} + 2 g h$ , so for lower value of $g$ the velocity will be less.
5. So, the packet dropped from height $h$ above the poles will take less time to reach the surface of the earth.	5. So, the packet dropped from height $h$ above the equator will take more time to reach the surface of the earth.

Identical packets are dropped from two airplanes, one above the equator and the other above the north pole, both at height h. Assuming all conditions are identical, will those packets take the same time to reach the surface of the earth. Justify your answer.

Identical packets are dropped from two airplanes, one above the equator and the other above the north pole, both at height $h$ . Assuming all conditions are identical, will those packets take the same time to reach the surface of the earth. Justify your answer.