Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d = R 2 from the surface of earth, if its weight on the surface of earth is 200 N , will be : (Given R = radi

Question

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

TestHub · Accepted Answer

The acceleration due to gravity with depth is
$g^{'} = g (1 - \frac{d}{R})$
The given data is
$W = 200 N d = \frac{R}{2}$
Let the weight be at the given depth, $W'$ . Hence, the value is
$m g^{'} = m g (1 - \frac{\frac{R}{2}}{R}) = m (\frac{g}{2})$
The Weight $W'$ $= \frac{W}{2} = \frac{200}{2} = 100 N$

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