# Question #0944f

##### 2 Answers

#### Explanation:

If the value at the earth's surface is g, we knew from the law of universal gravitation that this can be calculated from the mass of the earth (M), the gravitational constant (G), and the radius of the earth (R).

At a radius of 2*R the new value for acceleration (let's call it a) will be equal to:

With a little algebra we can see that this can be written as:

Solving for a using the value we know for g.

Law of Universal Gravitation states that the force of attraction

#F_G =G (M_1.M_2)/r^2# .......(1)

where#G# is the Gravitational constant.

It has the value#6.67408 xx 10^-11 m^3 kg^-1 s^-2#

If one of the objects is earth, mass

#F_G =G (M_e.m)/R^2# ......(2)

where#R# is radius of earth.

Comparing with equation

#"Weight"=mg# , we get

#g= (GM_e)/R^2=9.8ms^-2# .....(3)

When the object is located at a height equal to radius of earth, its distance from centre of the earth is

#F_G =G (M_e.m)/(2R)^2#

If

#g^'= 1/4(GM_e)/R^2# .........(4)

Dividing (4) by (3) and rearranging we get

#g^'=g/4#

#g^'=9.8/4=2.45ms^-2#