Question

Objects 1 and 2 attract each other with a gravitational force

of 18.0 units. If the distance separating Objects 1 and 2 is
changed to one-third the original value, then the new
gravitational force will be units.

Answer 1

F' = 162 units

Step-by-step explanation:

The gravitational force of attraction between the two objects is given by Newton's Gravitational law through the following formula:

`F = (Gm_(1)m_(2))/(r^(2))\\\\`

where,

F = gravitational force = 18 units

G = Gravitational Constant

m₁ = mass of object 1

m₂ = mass of object 2

r = distance between objects

Therefore,

`18 = (Gm_(1)m_(2))/(r^(2))------ eqn (1)\\\\`

Now, if we change the value of distance to one-third of original value, then:

r' = r/3

`F' = (Gm_(1)m_(2))/(((r)/(3))^(2))\\\\F' = (9)((Gm_(1)m_(2))/(r^(2)))`

using eqn (1):

F' = 9(18 units)

F' = 162 units