Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth from the surface of the earth, if its weight on the surface of the earth is 200 N, will be (Given R = radius of earth) [2023]

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Solution

Q.
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 the earth, if its weight on the surface of the earth is 200 N, will be (Given R = radius of earth) [2023]

1 400 N

2 500 N

3 300 N

4 100 N

Ans.
(4)

$M = \frac{W}{g} = \frac{200}{10} = 20 kg$

$Acceleration due to gravity at a depth$

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

$d = depth from surface, d = \frac{R}{2}$

$g' = g (1 - \frac{R / 2}{R}) = \frac{g}{2} = {5 m/s}^{2}$

$Weight = m \times g' = 20 \times 5 = 100 N$

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