The weight of a body at the surface of Earth is 18 N. The weight of the body at an altitude of 3200 km above the Earth's surface is (given, radius of Earth Re = 6400 km):

Given: Weight at Earth's surface = 18 N, height h = 3200 km, radius of Earth R = 6400 km. Find: Weight of the body at height h. Acceleration due to gravity at height h is g' = g [1 + hR ]^2 Hence, the weight at the given height will be mg' = mg [1 + hR ]^2 Substituting the values, mg' = 18 [1 + 12 ]^2 mg' = 8 N Therefore, the correct option is D and the weight is 8 N.

The weight of a body at the surface of Earth is 18 N. The weight… — Solution | JEE Physics

MCQEasyJEE 2023Variation with Altitude & Depth

The weight of a body at the surface of Earth is $18 \, \text{N}$ . The weight of the body at an altitude of $3200 \, \text{km}$ above the Earth's surface is (given, radius of Earth $R_e = 6400 \, \text{km}$ ):

A
$9.8 \, \text{N}$
B
$4.9 \, \text{N}$
C
$19.6 \, \text{N}$
D
$8 \, \text{N}$

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: Weight at Earth's surface = $18 \, \text{N}$ , height $h = 3200 \, \text{km}$ , radius of Earth $R = 6400 \, \text{km}$ .

Find: Weight of the body at height $h$ .

Acceleration due to gravity at height $h$ is

g' = \frac{g}{\left[1 + \frac{h}{R}\right]^2}

Hence, the weight at the given height will be

mg' = \frac{mg}{\left[1 + \frac{h}{R}\right]^2}

Substituting the values,

mg' = \frac{18}{\left[1 + \frac{1}{2}\right]^2}

mg' = 8 \, \text{N}

Therefore, the correct option is D and the weight is $8 \, \text{N}$ .

Common mistakes

Using a linear relation instead of the inverse-square relation is incorrect because weight at altitude depends on $\left(1+\frac{h}{R}\right)^{-2}$ . Use the full gravitational formula before substituting values.
Taking $h/R$ incorrectly is a common mistake. Here $\frac{3200}{6400} = \frac{1}{2}$ , not $2$ . Compute the ratio carefully before squaring.
Confusing mass with weight leads to errors. The mass remains constant, but the weight changes because $g$ changes with height. Apply the formula to weight directly as shown.

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Answer

Step-by-step solution

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