Question

The gravitational force between two giant lead spheres is 0.010 N when the centers of the spheres are 20 m apart. What is the distance between their centers when the gravitational force between them is 0.160 N?

Answer 1

The gravitational force between two giant lead spheres is 0.010 N when the centers of the spheres are 20 m apart. What is the distance between their centers when the gravitational force between them is 0.160 N?

​From the gravitational equation,

​F = G(m1.m2)/r^2, or

F.r^2 = G.m1.m2

​Considering the two instances detailed above

​F1.r1^2 = F2.r2^2

Substitutinbg values,

0.01*(20)^2 = 0.16*r2^2

4 = 0.16*r2^2

2 = 0.4*r2       (taking square roots)

r2 = 2/0.4 = 20/4 = 5

In the 2nd instance, they are now 5 m apart

Answer 2

let m1 is the mass of the first sphere and m2 is the mass of the second sphere

the gravitational force between them will be  f = m1m2/d^2  ( d is the distance between the centers of the

spheres)

so it will be 0.010=m1m2/400 and 400(0.010)=m1m2   (1)  and  0.160(d)^2=m1m2 (2) from the (1) and (2)

we have;  400(0.010)=0.160(d)^2 --->>>  d^2 = (400(0.010))/0.160   --->>> d^2 = 4/0.160 = 25

so d=sqrt25 = 5 m

so when the grav force is 0.160 N the distance will be 5 m

 

a second way solving this is as follows;

it is. (20/d)^2 = 0.160/0.010 --->>> (20/d)^2 = 16  -->>> taking sqrt  we get. 20/d = 4  so d=5 m