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The radius of the earth is r. at what distance above the earth's surface will the acceleration of gravity be 4.9 m/s2? the radius of the earth is . at what distance above the earth's surface will the acceleration of gravity be 4.9 m/s2? 0.50r 0.41r 2.0r 1.0r 1.4r

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The radius of the earth is R. At what distance above the earth's surface will the acceleration of gravity be 4.9 m/s^2?
A) 0.41R
B) 0.50R
C) 1.0R
D) 1.4R
E) 2.0R
A

Answer:

Height will be 0.41 r

Explanation:

We have given acceleration due to gravity at any height is [tex]g_{new}=4.9m/sec^2[/tex]

Radius of the earth = r

We know that acceleration due to gravity at any height is given by

[tex]g'=\frac{GM}{(R+h)^2}[/tex]----eqn 1

And acceleration due to gravity at earth [tex]g=\frac{GM}{R^2}[/tex]----eqn2

Dividing eqn 2 by eqn 1

[tex]\frac{g}{g'}=\frac{(r+h)^2}{r^2}[/tex]

[tex]\frac{9.8}{4.9}=\frac{(r+h)^2}{r^2}[/tex]

[tex]2r^2=(r+h)^2[/tex]

[tex]\sqrt{2}r=h+r[/tex]

h = 0.41 r

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