Question

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

Answer 1

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 2

Height will be 0.41 r

Step-by-step explanation:

We have given acceleration due to gravity at any height is
`g_(new)=4.9m/sec^2`

Radius of the earth = r

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

`g'=(GM)/((R+h)^2)`----eqn 1

And acceleration due to gravity at earth
`g=(GM)/(R^2)`----eqn2

Dividing eqn 2 by eqn 1

`(g)/(g')=((r+h)^2)/(r^2)`

`(9.8)/(4.9)=((r+h)^2)/(r^2)`

`2r^2=(r+h)^2`

`√(2)r=h+r`

h = 0.41 r