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JEE Main 202324 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
24 January
Shift
Morning Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2023 · 24 January · Morning Shift · Physics · Gravitation

The weight of a body at the surface of earth is 18N . The weight of...

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)

Options

  1. A9.8N9 . 8N
  2. B4.9N4 . 9N
  3. C19.6N19 . 6N
  4. D8N8N

Correct answer

D. 8N8N

Step-by-step solution

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)⇒ m{g}^{'} = \dfrac{4}{9} ( mg )

=49×18= \dfrac{4}{9} \times 18

=8N= 8N

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