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7.Gravitation
hard
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?
A
$75 \mathrm{~N}$
B
$375 \mathrm{~N}$
C
$300 \mathrm{~N}$
D
$225 \mathrm{~N}$
(JEE MAIN-2024)
Solution
$\text { At surface: } \mathrm{mg}=300 \mathrm{~N}$
$\mathrm{~m}=\frac{300}{\mathrm{~g}_{\mathrm{s}}}$
$\text { At Depth } \frac{R}{4}: g_d=g_s\left[1-\frac{d}{R}\right]$
$g_d=g_s\left[1-\frac{R}{4 R}\right]$
$\mathrm{g}_{\mathrm{d}}=\frac{3 \mathrm{~g}_{\mathrm{s}}}{4}$
$\text { weight at depth } \quad=\mathrm{m} \times \mathrm{g}_{\mathrm{d}}$
$=\mathrm{m} \times \frac{3 \mathrm{~g}_{\mathrm{s}}}{4}$
$=\frac{3}{4} \times 300$
$=225 \mathrm{~N}$
Standard 11
Physics
