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Q.

Assuming earth to be $a$ sphere of uniform mass density, how much would a body weigh half way down the centre of the earth, if it weighed $100 N$ on the surface?

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a

$50 N$

b

$10 N$

c

$100 N$

d

$25 N$

answer is A.

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Detailed Solution

Given, $m g = 100 N \Rightarrow g^{'} = g (1 - \frac{a}{R})$

$d = \frac{R}{2} \Rightarrow \frac{d}{R} = \frac{1}{2}$

$g^{'} = g (1 - \frac{1}{2}) = \frac{g}{2}$

$m g^{'} = \frac{m g}{2} = \frac{100}{2} = 50 N$

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