A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth? [2019]

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Solution

Q.
A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth [2019]

1 100 N

2 150 N

3 200 N

4 250 N

Ans.
(1)

Acceleration due to gravity at a depth d,

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

For $d = \frac{R}{2} \Rightarrow g_{d} = g (1 - \frac{R / 2}{R}) = \frac{g}{2}$

Required weight $W' = m g_{d} = \frac{m g}{2} = \frac{W}{2} = \frac{200}{2} = 100$ $N$

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