Amit buys few grams of gold at the north pole as per instruction of one of his friends.He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold brought? If not, why?
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Amit buys few grams of gold at the north pole as per instruction of one of his friends.He hands over the same when he
Answer:
This is an interesting question that involves physics and geography. The answer is that the friend will not agree with the weight of gold brought by Amit, because the weight of an object depends on the gravitational force exerted on it by the Earth, and this force varies with latitude.
The Earth is not a perfect sphere, but rather an oblate spheroid, meaning that it is slightly flattened at the poles and bulges at the equator. This causes the distance from the center of the Earth to the surface to be greater at the equator than at the poles. Since the gravitational force is inversely proportional to the square of the distance, this means that the gravitational force is weaker at the equator than at the poles.
Therefore, an object that weighs a certain amount at the north pole will weigh slightly less at the equator, because the gravitational force is reduced. According to [this calculator](^1^), a 10 gram gold bar would weigh 9.997 grams at the north pole and 9.973 grams at the equator, a difference of 0.024 grams. This difference may seem negligible, but it could matter for precise measurements or transactions involving large quantities of gold.
Another factor that affects the weight of an object on Earth is the centrifugal force caused by the Earth's rotation. The centrifugal force is perpendicular to the axis of rotation, and thus points outward from the equator and is zero at the poles. This force reduces the effective weight of an object by counteracting the gravitational force. The centrifugal force is proportional to the distance from the axis of rotation, which is also greater at the equator than at the poles. Therefore, an object that weighs a certain amount at the north pole will weigh even less at the equator, because the centrifugal force is increased.
According to [this article](^2^), the centrifugal force at the equator is about 0.3% of the gravitational force, which means that an object that weighs 10 grams at the north pole would weigh 9.97 grams at the equator, a difference of 0.03 grams. This difference is slightly larger than the one caused by the shape of the Earth, and together they account for a total difference of 0.054 grams for a 10 gram gold bar.
In summary, the weight of gold (or any object) varies with latitude due to the shape of the Earth and the centrifugal force caused by its rotation. An object that weighs a certain amount at the north pole will weigh less at the equator, and the difference will be proportional to the mass of the object. Therefore, Amit's friend will not agree with the weight of gold brought by Amit, and will claim that Amit has cheated him by bringing less gold than agreed.