A body weight W , is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height wi

Question

A body weight W , is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:

TestHub · Accepted Answer

Final distance from the centre of earth wil be $R + 9 R = 10 R$ .

Now acceleration due to gravity at any height(distance from centre r) is given by,

$g = \frac{G M}{r^{2}}$ .

Therefore,

$g^{'} = \frac{G M}{{(10 R)}^{2}}$

Now, value of $g$ at surface will be, $\frac{G M}{R^{2}}$ .

Hence,

$g^{'} = (\frac{g}{100})$ .

Then, $W^{'} = m g^{'} = \frac{m g}{100} = \frac{W}{100}$

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