Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $\mathrm{d}=\frac{\mathrm{R}}{2}$ from the surface of earth, if its weight on the surface of earth is 200 N, will be: (Given $\mathrm{R}=$ Radius of earth)

JEE Main · 2023 · 10 Apr 2023 · Shift 1 · Gravitation

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth

d = \frac{R}{2}

from the surface of earth, if its weight on the surface of earth is 200 N, will be:
(Given

R =

Radius of earth)

(A)400 N
(B)500 N
(C)300 N
(D)100 N✓ Correct

Answer: (D)

Solution

Inside a uniformly dense Earth the gravitational acceleration falls linearly with depth,

g^{'} = g (1 - \frac{d}{R})

. At

d = \frac{R}{2}

this gives

g^{'} = \frac{g}{2}

, so the weight is halved. Hence

W^{'} = \frac{200}{2} = 100

JEE Main · 2023 · 10 Apr 2023 · Shift 1 · Single correct option

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