Gravitation

JEE Main level, single correct, medium

70 of 223

Question 70 of 223

The weight of a body at the surface of earth is 18N18N. The weight of the body at an altitude of 3200km3200km above the earth's surface is (given, radius of earth Re=6400km{R}_{e}=6400km)

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Answer: (D) 8N8N

As height of the object is considerable compared to the radius of the earth, therefore approximation formula can not be used.
So weight at given height,
F=mg′=GMm(R+R2)2=49GMmR2F=m{g}^{'}=\dfrac{GMm}{{\left(R+\dfrac{R}{2}\right)}^{2}}=\dfrac{4}{9}\dfrac{GMm}{{R}^{2}}
⇒mg′=49(mg)\Rightarrow m{g}^{'}=\dfrac{4}{9}(mg)
=49×18=\dfrac{4}{9}\times 18
=8N=8N

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