Amit buys few grams of gold at the poles as per the 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 bought? If not, why?

[Hint: The value of g is greater at the poles than at the equator.]

Sciences - Main Course Book

Chapter 10. Gravitation




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Mass of the object remains same every where.
       g = G M1 M1 / d²

     M1 and M2 are masses of the bodies.  d = distance between Earth center and the person on the surface.

     The  distance d is less at the poles.  So  the gravity g' is more at the poles than at the equator.  Now, the gold bought at the  poles reads W grams weight.  The mass of the gold purchased is  W/g'  grams.

     The gravity at the equator  is g.   The weight =  W/ g' * g = W * g / g' .

Since g < g',  the weight will be < W.   So the weight of the gold as shown by the machine at the equator will be less.

   So the person will have paid more at the poles.  Same mass of gold will cost less at the equator.

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