Gravity Reduce the gravity once again

Classical Mechanics Level 3

How much below the surface of the Earth does the acceleration due to gravity reduce by 36% of its value on the surface of the Earth.

DETAILS AND ASSUMPTIONS:

1) Take the radius of the Earth as 6400 km.

The answer is 2304.

2 solutions

Sravanth C.
Mar 17, 2015

Here,

${ g }_{ h }=g-\frac { 36g }{ 100 } =\frac { 64g }{ 100 }$

But, ${ g }_{ h }=g\left( 1-\frac { d }{ R } \right)$ or, $d=\frac { \left( g-{ g }_{ h } \right) R }{ g }$

${ g }_{ h }=g\left( \frac { \left( g-\frac { 64 }{ 100 } g \right) 6400 }{ g } \right)$

$d=g\left( \frac { 100-64 }{ 100 } \times 6400 \right) =2304\quad km$

I used the following equation ???

The following formula approximates the Earth's gravity variation with altitude:

Gh=Go (Re/(Re + h)^2

Where

Gh is the gravitational acceleration at height h above sea level.

Re is the Earth's mean radius.

Go is the standard gravitational acceleration.

this gives 1600 km >>>

Ossama Ismail - 6 years, 2 months ago

Sir ,please see that, your formula must be used when the acceleration due to gravity is asked above the surface of the Earth, not Below the surface of the Earth.

Sravanth C. - 6 years, 2 months ago

Suprem S.Nalkund
Mar 17, 2015

No need fo this much of work, its logical for. 6400 gravity=100% so. 100%=6400 36%=? 6400×36/100=2304

Yeah! Thanks! But your's is logical!

And, as this question is quite easy your solution works.

But, yes you're right.

Please do up vote my solution too!

Thanks again @Suprem s.nalkund . . .

Sravanth C. - 6 years, 2 months ago

Gravity Reduce the gravity once again

The answer is 2304.

2 solutions

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