Question

A body of weight 500n on the surface of the earth how much would it weight halfway below the surface of the earth

Answer 1

Explanation:

as depth increases the value of g decreases

Answer 2

Given :

A body of weight 500 N on the surface of the earth .

To Find :

How much would it weight halfway below the surface of the earth .

Solution :

We know , weight on the surface of earth id given by :

$W=mg$

Here , g is acceleration due to gravity at the surface of earth and given by

$g=10\ m/s^2$ .

Therefore ,

$m=\dfrac{W}{g}\\\\m=\dfrac{500}{10}\\m=50\ kg .$

Now , variation of gravity inside the earth surface is given by :

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

Here , $d=\dfrac{R}{2}$ .

So ,

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

So , weight halfway below the surface of the earth is :

$W'=mg'\\W'=50\times 5\ kg\\W=250\ N$

Learn More :

Gravitation

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