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 ?

Correct answer: D. 225 ~N aligned & At surface: mg=300 N & m= 300 g_ s & At Depth R 4 : g_ d =g_ s [1- d R ] & g_ d =g_ s [1- R 4 R ] & g_ d = 3 g_ s 4 aligned weight at depth =m × g_ d aligned & =m × 3 g_ s 4 & =(3)/(4) × 300 & =225 N aligned

JEE Main 20246 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 6 April
Shift: Evening Shift
Subject: Physics
Chapter: Gravitation

JEE Main 2024 · 6 April · Evening Shift · Physics · Gravitation

Assuming the earth to be a sphere of uniform mass density, a body...

Assuming the earth to be a sphere of uniform mass density, a body weighed

300 \mathrm{~N}

on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

Options

A $75 \mathrm{~N}$
B $300 \mathrm{~N}$
C $375 \mathrm{~N}$
D $225 \mathrm{~N}$

Correct answer

D. $225 \mathrm{~N}$

Step-by-step solution

\begin{aligned} & \text{ At surface: } \mathrm{mg}=300 \mathrm{ N} \\ & \mathrm{ m}=\frac{300}{\mathrm{ g}_{\mathrm{s}}} \\ & \text{ At Depth } \frac{\mathrm{R}}{4}: \mathrm{g}_{\mathrm{d}}=\mathrm{g}_{\mathrm{s}}\left[1-\frac{\mathrm{d}}{\mathrm{R}}\right] \\ & \mathrm{g}_{\mathrm{d}}=\mathrm{g}_{\mathrm{s}}\left[1-\frac{\mathrm{R}}{4 \mathrm{R}}\right] \\ & \mathrm{g}_{\mathrm{d}}=\frac{3 \mathrm{ g}_{\mathrm{s}}}{4}\end{aligned}

weight at depth

\quad=\mathrm{m} \times \mathrm{g}_{\mathrm{d}}

\begin{aligned} & =\mathrm{m} \times \frac{3 \mathrm{ g}_{\mathrm{s}}}{4} \\ & =\frac{3}{4} \times 300 \\ & =225 \mathrm{ N}\end{aligned}

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