Physics · Gravitation

JEE Main 2024 — 6 April, Shift 2 — Question 35

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth?

  1. Option A:

    75 N

  2. Option B:

    375 N

  3. Option C:

    300 N

  4. Option D:

    225 N

    Correct

Answer: D

Step-by-step solution

At surface:

mg=300 N\mathrm{mg}=300 \mathrm{~N} m=300 gs\mathrm{m}=\frac{300}{\mathrm{~g}_{\mathrm{s}}}

At Depth R4:gd=gs[1−dR]\frac{R}{4}: g_{d}=g_{s}\left[1-\frac{d}{R}\right] gd=gs[1−R4R]g_{d}=g_{s}\left[1-\frac{R}{4 R}\right]

gd=3gs4g_{d}=\frac{3 g_{s}}{4}

weight at depth \begin{aligned} & =\mathrm{m} \times \mathrm{g}{\mathrm{d}} & =\mathrm{m} \times \frac{3 \mathrm{~g}{\mathrm{s}}}{4} & =\frac{3}{4} \times 300 & =225 \mathrm{~N} \end{aligned}$$

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Subject
Physics
Chapter
Gravitation
Topic
Gravitational Field and Gravity